More artichoke questions

[gemfyre]

I picked and tried my first fresh, homegrown artichoke and it was lovely. It's now flowering profusely (when I say flowers, I mean the green, edible bit, not the actual flower). The bracts open up before it gets very big so when I pick them they're a lot smaller than the ones I see in stores. Is there anyway I can make them get bigger? Or is this probably just an issue with the variety of artichoke I have (no idea what the variety is, I bought it from Bunnings for $5 and the tag just said 'artichoke').

Thanks for your help guys.