Preheat the oven to 400°F.
In a 3-quart baking dish, toss cherry tomatoes, zucchini, onion, and garlic with olive oil.
Season vegetables with garlic powder, crushed red pepper flakes, kosher salt, and black pepper.
Place the block of feta cheese in the center of the vegetable mixture and season it lightly with salt and pepper.
Bake at 400°F until tomatoes burst and feta softens, about 30 minutes.
Increase oven temperature to 450°F and bake an additional 10 minutes until feta is golden brown.
While baking, bring a large pot of salted water to a boil and cook pasta until al dente, about 10-12 minutes.
Reserve 1/2 cup of the pasta cooking water before draining the pasta.
Remove feta and vegetables from the oven; use a fork to mash feta into a creamy sauce with the roasted vegetables.
Add the drained pasta to the baking dish and toss to coat with the sauce.
If sauce is too thick, add reserved pasta water 1 tablespoon at a time until desired consistency is reached.
Garnish with fresh basil and grated Parmesan cheese before serving.