Rinse the artichokes in cold water. Bend back the green petals and snap them off all the way down to the light green and yellow leaves. Cut off the top cone of petals and the green part of the base. Cut the artichokes in half, if the choke and thistle look spiky, remove them. Otherwise, just put in acidulated water.
Coat a saucepan with 2 tablespoons olive oil and place over medium heat. Blot the artichokes dry then add them to the pan. Add the garlic, shallot, lemon slices, bay leaves and red pepper flakes. Pour in the stock, cover, and let simmer for 8 minutes to soften the artichokes. Remove the lid and add the olives, basil, tomatoes and butter, stir to incorporate. Add the peas and remaining oil; season again with salt and pepper. Cook pasta al dente and top with the baby artichoke sauce. Sprinkle with grated cheese before serving.
2001 Television Food Network, G.P. All Rights Reserved