Prepare the broccoli. Cut the broccoli into small florets. Peel the tougher exterior from the stalk and finely chop the tender center.
Toast the breadcrumbs. Heat 1 tablespoon olive oil in a small skillet over medium heat. Add the breadcrumbs and cook, stirring frequently, until golden and crisp. Remove from the heat and stir in the lemon zest, if using. Set aside.
Cook the broccoli. Bring a large pot of salted water to a boil. Add the broccoli and cook until very tender. Remove with a slotted spoon, reserving the cooking water.
Make the sauce. Heat 3 tablespoons olive oil in a large skillet over medium-low heat. Add the garlic and red pepper flakes and cook gently until fragrant.
Add the anchovies and cook, stirring, until they dissolve into the olive oil.
Add the cooked broccoli and a splash of its cooking water. Use the back of a wooden spoon to crush some of the broccoli, leaving some florets intact.
Cook the pasta. Return the broccoli cooking water to a boil. Cook dried pasta until very al dente, or cook fresh homemade rigatoni for approximately 3–5 minutes. Reserve at least 1 cup pasta water before draining.
Finish the pasta. Transfer the pasta to the skillet. Toss over medium heat, gradually adding enough pasta water to create a creamy, glossy broccoli sauce that coats the pasta.
Taste and adjust the seasoning. Be careful with additional salt because the anchovies are already salty.
Divide among bowls and finish generously with the crispy breadcrumbs and, if desired, a drizzle of extra-virgin olive oil. Serve immediately.