Separate the broccoli “treetops” from the stems. Cut or break the tops into 3/4-inch florets. Peel the knobby stems and slice them 1/4-inch thick.
In a large deep skillet or saucepan, combine olive oil and garlic then turn heat to medium-high. Cook until the garlic is fragrant and just beginning to turn golden. Add the anchovies, if using, lemon zest and pepper flakes and cook for 2 more minutes, using a spoon or spatula to break the anchovies into tinier bits. Add a glug of wine, if using, and cook until it disappears. Add the broccoli and stems, kosher salt, and many grinds of black pepper, and cook, stirring often, for 5 minutes; the broccoli will get darker in color. Add the dried pasta and water and bring the mixture to a simmer. Cover the pan and for 12 minutes, or until the pasta is al dente. Lift the lid and stir a couple times while the pasta cooks, just to ensure it’s cooking evenly. Remove the pan from the heat and let it rest, lid on, for 5 minutes.
Remove lid, and taste for seasoning, adding more salt if needed. Finish with lemon juice, a drizzle of olive oil, additional black pepper, and grated parmesan. Spoon onto plates and serve with more parmesan.