Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1 cup cooking water, then drain.
Meanwhile, heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the cauliflower, season with salt and cook, without stirring, until it starts browning around the edges, 5 to 8 minutes. Stir once or twice and cook until well browned and softened, 5 to 7 more minutes. Push some of the cauliflower to one side of the pot, add the garlic, red pepper flakes and anchovies and cook until the garlic is lightly browned, about 30 seconds. Stir in the tomatoes with their juices and season with 1/4 teaspoon salt. Bring to a simmer and cook until slightly thickened, 1 to 2 minutes. Stir in the capers and olives.
Add the pasta and 1/2 cup of the reserved cooking water to the sauce; cook, stirring, about 1 minute, adding more cooking water as needed to loosen. Season with salt and stir in the parsley. Drizzle each serving with olive oil and top with parmesan.