Bring a large pot of salted water to a boil over high heat. Add the broccoli and cook until tender, about 4 minutes. Using a slotted spoon, transfer the broccoli to a blender or food processor.
Return the water to a boil. Add the pasta and cook until al dente according to the package instructions. Reserve 1¼ cups of pasta water.
Meanwhile, add the basil, garlic, pine nuts, olive oil, salt, and Parmesan to the blender with the broccoli and blend until smooth.
Slowly pour in the reserved pasta water a little at a time, until a sauce consistency forms (about 1 cup).
Drain the noodles. Transfer the sauce back to the pot. Add the pasta to the sauce and toss to coat.