Preheat the oven to 400°F. Line a large baking sheet with parchment paper.
Place the feta, peppers, tomatoes, onion, thyme and garlic in on the prepared sheet pan. Season everything with black pepper and drizzle with olive oil.
Bake in the preheated oven for 45 minutes, or until the vegetables are tender and the feta is melty.
Meanwhile, bring a large pot of heavily salted water to a boil. Cook the pasta until al dente according to package directions. Reserve 1 cup pasta water, drain and return the pasta to the pot, covered.
Remove the roasted garlic bulb and thyme sprigs and set aside until cool enough to handle.
Transfer the roasted vegetables and feta into a blender. Carefully squeeze the roasted garlic into the blender and remove the thyme leaves from the stem. Add the reserved pasta water and blend for 2 minutes, or until smooth and creamy.
Transfer on top of the cooked pasta and toss until well combined. Serve immediately with more freshly cracked black pepper, if desired.
