Heat oven to 400°F.
In a small pot, combine garlic and oil, heat over low flame and gently cook until garlic is light golden in color and very fragrant, about 10-15 minutes. Remove garlic cloves and reserve.
Pile cauliflower on baking sheet and dress with lemon juice, about 3-4 tablespoons of the garlic-infused oil, thyme, salt and pepper. Toss to combine and spread florets out in a single layer. Roast to brown at edges and tender, 20-25 minutes. Cover with Parmigiano-Reggiano and roast 5 minutes more. Turn oven off.
Meanwhile, boil parsnips in salted water to tender, 10-15 minutes. Purée in a food processor with the garlic cloves.
Bring a large pot of water to a boil for the pasta.