In a large pot, bring 4 quarts water and 2 tablespoons salt to a boil. Peel the broccoli stems, reserving any leaves, and cut crosswise into ½-inch rounds. Add the stems and leaves to the boiling water and cook until fully tender, about 10 minutes.

Stir in the spinach and cook until wilted, about 20 seconds. Using a slotted spoon, transfer the vegetables to a blender; reserve ½ cup of the cooking water. Keep the water at a boil.

Cut the broccoli florets into 1- to 1½-inch pieces. Add the florets to the boiling water and cook until crisp-tender, about 3 minutes.

Using the slotted spoon, transfer to a colander and rinse under cold water until cooled. Again keep the water at a boil.

To the blender, add the garlic, butter, capers, pepper flakes, ¾ teaspoon salt, 1 tablespoon of the lemon zest and the reserved broccoli cooking water.

Puree until smooth and bright green, about 30 seconds. Taste and season with salt and pepper.

Stir the rigatoni into the boiling water and cook until al dente. Reserve ½ cup of the cooking water, then drain.

Return pasta to the pot and add the broccoli florets, the broccoli puree, ¼ cup of the reserved cooking water, the remaining 1 tablespoon lemon zest and the cheese.

Cook over medium, stirring constantly, until the sauce thickens slightly and the pasta is well coated, 1 to 2 minutes. Remove from the heat. Taste and season with salt and pepper.