Preheat oven to 400°F.
Toss tomatoes, oil, thyme (or oregano), crushed red pepper and salt together in a 9-by-13-inch baking dish. Place feta in the center. Bake until the tomatoes are broken down and bubbling, about 30 minutes.
Add pasta to the baking dish. Whisk boiling water, tomato paste and garlic together in a measuring cup and pour it over the pasta. Stir to combine. Carefully cover with foil and bake until the pasta is tender, about 18 minutes. Remove from the oven and stir. Cover and let stand for 5 minutes before serving.