Adjust the oven rack to the lowest position, place a large rimmed baking sheet on the rack, and heat the oven to 450 degrees.

Place the garlic heads on a square of aluminum foil, drizzle with a small amount of oil, and wrap the foil tightly to create a sealed packet.

In a large bowl, toss the cauliflower wedges with oil, salt, pepper, and sugar until evenly coated.

Carefully remove the hot baking sheet from the oven and spread the cauliflower in an even layer. Place the foil-wrapped garlic on a corner of the sheet and roast until the cauliflower is tender and the bottoms are deeply browned, about 20 to 25 minutes.

While the vegetables roast, bring a large pot of salted water to a boil. Cook the campanelle until al dente, then reserve 1 cup of the cooking water before draining the pasta.

When the garlic is cool enough to handle, squeeze the roasted cloves from their skins into a small bowl and mash them into a smooth paste. Whisk in the lemon juice, red pepper flakes, and the remaining teaspoon of olive oil.

Combine the drained pasta, roasted cauliflower, garlic mixture, Parmesan, and parsley in the pot. Toss gently to combine, adding the reserved pasta water as needed to create a light sauce that coats the noodles. Season with salt, pepper, and additional lemon juice to taste. Serve hot, topped with toasted walnuts.