1 cup olive oil, or more if needed
2 large heads broccoli, cut in 1-inch florets (about 6 cups)
1 tablespoon kosher salt, plus more for salting the pasta water
8 garlic cloves, roughly chopped
1 pound penne rigate (Penne rigate is my favorite because the ridges give it more texture.)
1/2 cup shredded or grated Parmigiano-Reggiano cheese
2 tablespoons chopped Italian flat-leaf parsley, for garnish
I recommend sauteing the broccoli in a shallow saute pot, rather than in a saute pan. You'll be able to saute the vegetables properly and the pot will be big enough to accommodate the pasta after it and the broccoli are both cooked. If you don't have a saute pot, use a saute pan for the broccoli and combine the cooked pasta and broccoli in a large bowl.