A double-dose of broccoli never tasted so good.
Preheat the oven to 425°. On a baking sheet, toss the broccoli, 2 tbsp. oil, and the oregano; season with salt and pepper. Roast, turning once, until the broccoli is tender and browned in spots, about 20 minutes. Let the broccoli cool.
Bring a large pot of water to a boil. In a food processor, pulse 1/4 cup pine nuts and the garlic until chopped. Add 2 cups basil, 1/4 cup cheese, the lemon juice, and 1/2 tsp. salt. Pulse until finely chopped. With the machine running, drizzle in the remaining 1/3 cup oil until almost smooth. Add half the cooled broccoli. Pulse until finely chopped; season the pesto.
Salt the boiling water and add the pasta. Cook until al dente. Scoop out about 1/2 cup of the cooking water. Drain the pasta; return to the pot. Stir in the broccoli pesto and the remaining broccoli; add the cooking water as needed if the pasta is too dry. Season the pasta and sprinkle with the remaining 1/4 cup cheese and 3 tbsp. pine nuts and the chopped basil.