Clean the artichokes by removing all the tough outer leaves until you get to a pale yellow center. Peel the outer tough skin of the artichoke stems with a paring knife. Trim 1/3 off the tops of each artichoke and rub with lemon. Squeeze the lemon juice into a bowl of cool water and place all the cleaned artichokes in to prevent them from browning.
Place the fettuccine in salted boiling water. Stir to prevent the strands from sticking together.
Add the olive oil, garlic and chile, if using, to a saucepan and saute until golden. Remove the artichokes from the water and roughly chop. Add the chopped artichokes, cherry tomatoes, and wine to the pan. Once the wine has reduced, add the tomato puree, mint, and salt, to taste. Allow to simmer for approximately 15 minutes.
About 2 minutes before the fettuccine is at the 'al dente' stage, drain the pasta, reserving approximately 1 cup of pasta water. Add the fettuccine and pasta water to the pan. Then add the butter and Parmigiano cheese and cook all together for an additional 30 seconds. Serve immediately.