Fill a medium bowl halfway with water and the lemon juice. Set aside.
To prepare the artichokes, peel off a few layers of the tough, dark outer leaves from the artichokes, until you get to the lighter green leaves. Trim the stem, if present, so about a 1/2-inch remains. Cut off and discard the top 1/4 of the artichokes, then quarter them lengthwise. As each artichoke is cut, place it in the lemon water, cut side down, so it doesn’t brown.
Add 2 tablespoons olive oil to a saucepan over medium heat. Drain the artichokes and pat them dry. Add the artichokes to the pan along with the garlic, shallot, 2 tablespoons lemon zest and red pepper flakes; season with salt and pepper. Cook for about 1 to 2 minutes, stirring, then add the wine. Cook until wine is reduced by half, about 2 to 3 minutes. Add the stock, cover, and let simmer for 8 to 10 minutes, or until the artichokes have softened. Remove from heat; add the tomatoes and butter. Gently stir to mix well.
Meanwhile, in a small bowl mix together the basil and 3 tablespoons olive oil.
Prepare the pasta according to package directions. When drained, toss with the basil and olive oil mixture.
Add the artichoke mixture to the pasta, season with salt and pepper and gently toss to incorporate the ingredients. Serve with a sprinkling of Parmigiano-Reggiano and a drizzling of 1/2 tablespoon olive oil.