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 vegetables are baking, cook pasta al dente in salted water. Drain and reserve at least 1 cup of pasta water.
Gently stir the feta and vegetables. Mix in pasta adding just enough pasta water to make a creamy sauce.