3 pints cherry tomatoes, halved
1/2 cup plus 1 tablespoon extra-virgin olive oil
1/3 cup fine dry bread crumbs
1 teaspoon kosher salt, plus more for the pasta pot
1/4 teaspoon peperoncino flakes, or to taste
1 pound spaghetti, gemelli, or penne
10 plump garlic cloves, peeled and sliced
2 tablespoons chopped fresh Italian parsley
1 cup loosely packed basil leaves, shredded
1/2 cup freshly grated Parmigiano-Reggiano
4 ounces ricotta or ricotta salata
Arrange a rack in the center of the oven, and heat to 350. Toss the cherry tomato halves in a large bowl with 3 tablespoons of the olive oil. Sprinkle over tomatoes the bread crumbs, salt, and pepper flakes; toss well to coat evenly. Pour the tomatoes onto the parchment-lined sheet, and spread them apart in a single layer. Bake until the tomatoes are shriveled and lightly caramelized (but not dried out), about 25 minutes in all.
Meanwhile, fill a large pot with salted water, and heat to a rolling boil. When the tomatoes are nearly done, drop the pasta into the pot, stir, and return the water to a boil.
As soon as the pasta is cooking, our the remaining olive oil into a big skillet, set it over medium-high heat, and scatter in the sliced garlic. Cook for a minute or two, until it is sizzling and lightly colored, then ladle in about 2 cups of the pasta cooking water, and bring to a vigorous boil, stirring up the garlic. Let half the water evaporate, then lower the heat, stir in the chopped parsley, and keep the sauce barely simmering.
As soon as the tomatoes are done, remove them from the oven.
When the pasta is al dente, lift if from the water, drain for a moment, and drop it into the skillet, still over low heat. Toss pasta quickly with the garlic and parsley sauce in the pan, then slide the baked tomatoes on top of the pasta. Scatter the basil shreds all over, and toss everything together well, until the pasta is evenly dressed and the tomatoes are distributed throughout. Turn off the heat, sprinkle on the grated cheese, toss once more.
Serve the the shredded ricotta all over the top.