Melt the butter and 1 tablespoon olive oil in a small skillet over medium heat. Once the butter is melted, add the breadcrumbs and toast until golden brown and crispy, 2 to 3 minutes. Set aside.
Bring a large pot of water to a boil. Season aggressively with salt. Add the pasta and cook to al dente, 1 to 2 minutes less than the package recommends. Drain, reserving 1 cup of the pasta cooking water.
Heat the remaining 2 tablespoons olive oil in a large skillet over medium-high heat. Add the anchovies and cook, using a wooden spoon to break them up, until the anchovies begin to dissolve into the oil, 2 to 3 minutes. Reduce the heat to low. Add the garlic and chile flakes and cook, stirring, an additional 1 to 2 minutes, taking care not to burn the garlic. Stir in the tomatoes, olives, capers, 1/2 teaspoon salt and 1/4 teaspoon pepper. Bring to a simmer and cook until thickened, 10 to 15 minutes. Increase the heat to medium-high, then add the spaghetti and 1/4 cup to 1/2 cup of the pasta water. Cook, tossing, until the pasta is coated and the sauce begins to thicken, 1 to 2 minutes. Remove from the heat and stir in the parsley. Top with the toasted breadcrumbs and serve immediately.