Preheat oven to 425°F.
Toss vegetables with olive oil, garlic, and seasonings in a 9x13 baking dish. Nestle the block of feta into the middle of the veggies.
Roast for 15 minutes. Stir the vegetables and roast an additional 10-15 minutes or until vegetables are tender. Broil 2-3 minutes to lightly brown the cheese.
While the tomatoes are baking, cook pasta al dente in salted water. Reserve at least 1 cup of pasta water and drain well. Do not rinse.
Gently stir the feta and vegetables in the baking dish.
Add pasta water and stir, adding pasta water as needed to make a creamy sauce.
Stir in fresh basil, season with salt & pepper to taste, and serve.
