Cut off the top third and the bottom stem, right at the base, of each artichoke, so that they sit up straight.
Place each artichoke on a large square of heavy duty tinfoil (or double layer of regular tinfoil) and stuff 2 garlic cloves into the top of each.
Slightly spread the leaves apart with your fingers and drizzle each artichoke with olive oil, about 1 Tbsp or so.
Wrap the tinfoil up tightly around each artichoke and place on a baking tray and into the oven until nice and soft, about 1 hour and 15 minutes. It could be slightly less and could be slightly more.
Once the artichokes are roasted, let them cool until you can handle them.
Pull each leaf off the artichokes(you can scrape off all the meat with your teeth if you like!) until you get to the base. Pop the bottom part off, which will reveal some furry looking stuff. Once you scrape that off, you have the artichoke heart!
Repeat with remaining artichokes and thinly slice the hearts, and set aside. *^
Bring a large potof salted water to a boil, and cook the pasta until al dente, about 8-9 minutes.
While the pasta cooks, heat your oven to 400 degrees and toast the pine nuts until golden brown, about 5-7 minutes.
Heat the 1 tsp olive oil in a small pan on medium/high heat and sauté the garlic until just golden brown, about 1-2 minutes.
In a large bowl, toss together the cooked pasta, pine nuts, sauteed garlic, halved cherry tomatoes and sliced basil.
Combine the olive oil, fresh lemon juice, salt and pepper and pour over the salad, tossing until evenly coated.
Garnish with fresh, grated Parmesan cheese, if desired
*if you don't want to roast them yourself, use 1 cup of chopped canned artichokes marinated in olive oil.** If you want a good visual on how to roast, and peel, an artichoke check out this tutorial from Pinch My Salt