Rinse garlic head and remove outer papery skin. Cut top quarter off the garlic head so that the tops of the cloves are exposed. Place the garlic cut side up in a 12 inch square of foil, drizzle with 1/2 tsp of oil and wrap securely.
Adjust oven racks to middle and lower middle positions and heat oven to 400 degrees. Roast garlic on lower rack for 35 minutes. Let cool. Put second baking sheet in the oven for the last 10 minutes that the garlic is roasting.
Toss cauliflower with 1 Tbsp oil, 1/2 tsp salt, 1/4 tsp pepper and 1/8 tsp sugar. Using good oven mitts, take out the hot sheet and spread the cauliflower pieces on the hot sheet and roast for 10-15 minutes. Spread the roasted cauliflower on a cutting board and chop into 1/2 inch pieces.
Unwrap cooled garlic and squeeze the baked cloves into a small bowl, mash with a fork, stir in the lemon juice & pepper flakes and then slowly whisk in the remaining 2 Tbsp of olive oil.
Cook the pasta in salted water, drain, reserving some of of the pasta water and return pasta to the pot with the garlic lemon sauce, 2 Tablespoons of the reserved pasta water, parmesan, parsley and chopped walnuts. Adjust seasonings with salt, pepper, extra lemon or extra pasta cooking water if needed.