Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, 8 to 10 minutes. Drain and reserve about 1 cup of the pasta water.
In a 12-inch nonstick skillet, heat 1/4 cup of the extra-virgin oil over medium heat. Add the anchovy paste, red pepper flakes and garlic. Cook until aromatic, 2 minutes. Add the spinach and 3/4 teaspoon salt, and cook until wilted, about 3 minutes. Add the breadcrumbs and cook until lightly toasted, 2 to 3 minutes.
In a large serving bowl, toss together the breadcrumb mixture, cooked pasta and half of the cheese. Add in the reserved pasta water, if needed, to loosen the pasta. Drizzle with the remaining 1/4 cup of olive oil and sprinkle with the remaining cheese, and serve.