1Preheat the oven to 400°F. Line a large baking sheet with parchment paper.
2Place the feta, peppers, tomatoes, onion, thyme and garlic on the prepared sheet pan. Season everything with black pepper and drizzle with olive oil.
3Bake in the preheated oven for 45 minutes, or until the vegetables are tender and the feta is melty.
4Meanwhile, bring a large pot of heavily salted water to a boil. Cook the pasta until al dente according to package directions.
5Reserve 1 cup pasta water, drain and return the pasta to the pot, covered.
6Remove the roasted garlic bulb and thyme sprigs and set aside until cool enough to handle.
7Transfer the roasted vegetables and feta into a blender. Carefully squeeze the roasted garlic into the blender and remove the thyme leaves from the stem.
8Add the reserved pasta water and blend for 2 minutes, or until smooth and creamy.
9Transfer on top of the cooked pasta and toss until well combined. Serve immediately with more freshly cracked black pepper, if desired.