Boil the Broccoli: Cut 1 pound broccoli into small florets. Boil in a large pot of salted water for about 5 minutes, until fork-tender. Keep the water for later.
Make the Sauce: In a skillet, heat 3 tablespoons extra virgin olive oil over medium. Add 2 cloves garlic (grated) and ¼ teaspoons red pepper flakes, cooking briefly until fragrant. Add broccoli plus 1 cup of the cooking water. Simmer 8 to 10 minutes, then mash with a fork or blend until creamy.
Cook Pasta and Mix: Boil 12 ounces short pasta in the same broccoli water until just under al dente (about 1 minute less than the package). Drain, saving 1 cup of water. Add pasta to the skillet with the sauce, stir in ½ cup grated parmesan, and loosen with pasta water until glossy.
Finish and Serve: Taste, adjust salt, then top with basil and shaved parmesan. Serve hot and enjoy!
