Fill a large bowl with water and squeeze in the juice of a whole lemon. Add the rinds in the water as well.
Prepare the artichokes: Remove the tough outer leaves, about 5-6 layers, until you reach the leaves that are more soft and tender. Use a sharp knife to cut 1 inch off the top, as well as the bottom inch of the stem. Peel the tough outer layer of the stem with a paring knife or a veggie peeler. Slice the artichoke in half lengthwise. Use a small spoon (I used a grapefruit spoon) to scoop out the fuzzy center choke. Immediately place the artichoke halves in the lemon water, submerging on all sides to keep from browning.
After at least 10 minutes, remove the artichokes from the lemon water and pat dry in a kitchen towel.
Heat 1 inch of olive oil in a pan to 300 degrees F.
Add the artichoke halves to the pan cut side down so a little, and fry for 10-12 minutes. Flip the artichokes and fry for another 3-4 minutes until the leaves are crispy and a fork can easily be pierced through the thickest part of the stem.
Remove from the pan and sprinkle with salt and pepper. Serve with lemon wedges.