Pre-heat oven to 400 degrees and line a baking sheet with foil.
Place vegetables and garlic cloves on a baking sheet then drizzle with half the olive oil, salt, and pepper. Toss well then roast until tender, 18-20 minutes.
While vegetables are roasting, prepare pasta according to package instructions reserving 1/2 cup starchy cooking liquid. Strain pasta then return to the warm cooking pot.
Toss roasted vegetables into the pasta pot along with the reserved cooking liquid, remaining olive oil, parmesan, parsley, and chili flakes. Check for seasoning and adjust accordingly before serving.
While the vegetables are roasting, cook the pasta and reserve a bit of the salty, starchy cooking liquid for later. Once you drain the pasta, add it right back into the warm pot then toss in the roasted vegetables, olive oil, Parmesan cheese. Add just enough of the reserved cooking liquid to create a silky, smooth sauce then sprinkle with fresh parsley to serve.