In a small bowl combine the olive oil, garlic, lemon zest and juice, anchovy fillet, ½ teaspoon salt, and ¼ teaspoon pepper. Whisk to combine.

Set a large nonstick skillet over medium-high heat. Add the sausage and cook, breaking it up with a wooden spoon as needed, until browned and cooked through, about 6 minutes. Remove the sausage with a slotted spoon and transfer to a large mixing bowl.

While the sausage is cooking, bring a large pot of salted water to a boil over high heat and add the broccoli florets. Cook the broccoli until the water returns to a boil, about 1 minute. Remove with a slotted spoon, and transfer to the bowl with the sausage.

Return the pot of water to a boil. Add the rigatoni and cook according to package directions until al dente, about 8 minutes. Remove with a slotted spoon and add to the bowl with the broccoli and sausage.

Add the olive oil mixture to the bowl with the pasta and toss to combine. Serve immediately with finely grated parmesan and more olive oil, if desired.