1. Bring a large pot of water to a boil. Prepare an ice bath (a large bowl of ice and cold water).2. Salt the boiling water generously. Add the broccoli florets and boil for 3-4 minutes until bright green and tender-crisp.3. Using a slotted spoon, immediately transfer the broccoli to the ice bath to “shock” it. Once cooled, drain and roughly chop the broccoli.4. Bring the same pot of water back to a boil. Add the orecchiette and cook according to package directions until al dente.5. While the pasta cooks, heat the olive oil in a large skillet over medium-low heat. Add the anchovy fillets and use a wooden spoon to break them up. Cook until they dissolve into the oil (about 2-3 minutes).6. Add the sliced garlic and red pepper flakes. Cook for 2-3 minutes, stirring constantly, until the garlic is fragrant and pale golden. Do not let it brown.7. Add the chopped broccoli to the skillet. Sauté for 4-5 minutes, stirring, to infuse it with the oil.8. When the pasta is al dente, reserve 1 cup of the starchy pasta water. Drain the pasta (or use a spider to transfer it directly into the skillet).9. Add the pasta to the skillet with the broccoli. Add 1/2 cup of the reserved pasta water and the grated Pecorino.10. Turn off the heat. Stir and toss vigorously for 1-2 minutes. The pasta water and oil will emulsify, creating a light, creamy sauce that coats the pasta. If it seems dry, add more pasta water, a tablespoon at a time.11. Serve immediately, topped with extra Pecorino cheese and black pepper.