In a large pot, bring 4-6 quarts of water to boil, over high heat. (Be sure to use enough water to hold all of the pasta and broccoli without crowding, since you will be cooking them together in the same pot.)
When the water reaches a rolling boil, add 1 tablespoon of sea salt. Add the pasta and boil for 2 minutes, then add the chopped broccoli.
Cook for another 8 minutes, or until the pasta is just al dente and the broccoli is tender and starting to fall apart.
While the pasta and vegetables cook, heat the olive oil and garlic in a small saucepan over medium heat. When the garlic is fragrant and lightly golden, add the red pepper flakes; cook until fragrant, another 30 seconds. Remove from heat.
When the pasta and broccoli are done, drain them well and transfer them back into the pot. Add the olive oil infused with garlic and red pepper flakes, mix well until evenly distributed. Add pine nuts and season with sea salt and freshly ground black pepper to taste.
Serve with freshly grated Parmigiano Reggiano cheese.