This is a guest post. My buddy Mousetrap has graciously decided to offer his insight into this style of cooking, so you'll be hearing from him from time to time. This, personally, is a FANTASTIC tip. A panini press is grossly expensive for no good reason, and this tip gets the same effect (if missing the stupid scoremarks that nobody really cares about anyway) for basically free.
A panini is a grilled and pressed sandwich, and one doesn't need expensive equipment to make them, nor does it take much longer than throwing a sandwich together. It occurs to me that some of you have never had this wonderful Italian invention. This is unacceptable.
A few words on how to build your sandwich before we discuss the cooking method. First and most important is the bread. The sandwich is going to take a bit of punishment, so we want something crusty, something that you can cut a little thicker than normal. Most of all, though, we want something fresh. This is key, because factory breads do not work well for this. They are eighty percent(or more) puffed air, making them a bit too flimsy for the punishment they need to go through. Fresh Italian, french, or Ciabatta is best. With the exception of the ciabatta, which was probably invented for this sole purpose, you may want to slice the bread as much as an inch thick. Second, make sure that any oily ingredients you have, such as cheese or pepperoni, are shielded from the bread by something else. With the pressure we're going to be putting it through, there's a chance that the oil will leak out or through. it won't affect the flavor per se, but it'll take longer to cook. Third and last. Try to be even with the sandwich. if you use vegetables, be sure they're sliced thin. Build an even sandwich so when it's pressed down, it cooks evenly.
Alright. Now to the cooking method. Go get a brick.
Wait! No! Keep reading, I'm serious! Get a brick, and ensure it's clean and dry. Wrap it in a double layer of aluminum foil. Pre-heat a skillet on your stovetop on medium heat. Place the sandwich evenly on the skillet, then put the brick on top of the sandwich. Cooking time will vary but probably won't be more than a few minutes a side. Now since we don't have an expensive sandwich press, you'll have to do one of two things. Preheat the brick in your oven, or flip the sandwich midway. Personally I recommend the second method.
"Mousetrap," you're saying. "I'm not cooking with masonry." Well, stop talking, because I can't actually hear you. What you should do is get a cheap aluminum pie plate. The best way to do this is to buy a pie, enjoy the pie, then keep the plate around after it's gone. Fill the pie plate with something heavy such as stones or rice, and use that to press your sandwich down. I warn you, the sandwich won't be as thin as it would if you were to use the afforementioned brick method.
This sample recipe is one I use constantly. It's a cheap version of the classic "Italian" sandwich. The traditional trio of meats is cappicola, pepperoni, and proscuitto. I don't have the money to eat these things as often as I want. I make due with salami, pepperoni, and deli-sliced ham. First slice your italian bread three quarters of an inch thick or so. Cutting with a slight diagonal bias will help you in the long run. Place a thin layer of ham down first, just enough to give a taste to the sandwich. Next, fold slices of sandwich pepperoni in half and arrange as a layer. Top with provolone cheese. Be careful not to go overboard on this, one slice of provolone, cut into halves, is probably more than enough for you. Fold salami in the same way, and layer it on top of that. Spread a thin layer of italian dressing, to taste. This is the step where you would add such things like lettuce. You're welcome to try, but personally I never have. I never felt that it needed it. The sandwich is done when it's golden brown, and the cheese just begins to leak out of the sandwich. look for little beads of provolone around the edge.
Experiment and find what you enjoy best out of your sandwich. there's millions of ways to make a panini. You may have to slice or shred some ingredients if they prove too thick. Also, try using fresh herbs or spices to add flavor instead of loading it with sauce. The less that leaks out of your sandwich, the better.
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An addendum to this, which me and the Mousetrap discussed to some length, is this: It's a generally accepted fact that brushing the bread with a bit of either mayo (less good) or egg white (preferable) before cooking leads to a crisper sandwich. He's never tried it, and I've only used the egg white method to shore up my garlic bread, but like I said it's a generally accepted fact. Take it as you will.
For the pedants out there, his italian panini is called a BMT, and personally I find the depth of flavor to be surprising, since the sandwich doesn't have to rely on all spicy meats and the ham is a good equalizer. If you really want the extra heat of a full italian sandwich, toss a tiny bit of roasted red peppers on it, layered with the cheese. Most of the flavor from proscuitto comes from red peppers, so it'll have the same bite but with a bit of extra texture. Pound for pound, the peppers are also far cheaper and you'll get more interesting uses out of them.