In a medium pot, bring milk and broth to a rapid simmer. Add cauliflower and cook, covered, until just tender, 7 minutes. Using a slotted spoon, transfer 3 cups cauliflower to a bowl. Cook remaining cauliflower (4 cups), covered, until soft, 6 to 8 minutes longer. Transfer soft cauliflower to a blender with 1 1/2 cups cooking liquid, 2 tablespoons Parmesan, and 1 teaspoon salt. Blend until smooth; pulse in heavy cream.
In a large pot of salted boiling water, cook pasta according to package instructions. Reserve 1 cup pasta water. Drain and return pasta to pot. Stir in butter, cauliflower puree and florets, and peas. Add pasta water if necessary to create a creamy sauce that coats the pasta. Season with salt and pepper and serve with remaining 2 tablespoons Parmesan.