6 thin slices prosciutto or speck (cut crosswise into ¼-inch strips)
½ oz. finely grated Parmigiano-Reggiano (1/2 cup)
1 Tbs. chopped fresh flat-leaf parsley
Bring a large pot of well-salted water to a boil.
Meanwhile, heat 1 Tbs. of the butter and 1 Tbs. of the oil in a 12-inch skillet over medium heat. Add half of the cauliflower, flat side down in a single layer, and season lightly with salt. Cook until golden brown on one side, about 2 minutes. Flip and cook until the cauliflower is tender, about 3 minutes more. Transfer to a plate. Repeat with the remaining cauliflower, 1 Tbs. butter, and 1 Tbs. oil; set aside.
Boil the pasta according to package directions until al dente.
Meanwhile, melt 1 Tbs. of the butter in the skillet over medium heat. Add the anchovies, rosemary, garlic, and pepper flakes. Cook, stirring, until the garlic is softened, about 2 minutes. Add the broth, and cook until reduced by half, 2 to 3 minutes more.
Reserve ½ cup of the pasta water, and then drain the pasta. Add the pasta to the skillet along with the prosciutto, half of the cheese, and the remaining 1 Tbs. butter; toss until the butter is melted. Add the cauliflower, toss to combine, and season to taste with salt. Add some pasta water to loosen the sauce, if necessary. Serve topped with the remaining cheese and the parsley.