Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions until al dente. In the last 3 minutes of cooking, add the broccoli florets to the pot. Drain the pasta and broccoli, reserving about ½ cup of the pasta water.
In the same pot, return the drained pasta and broccoli. Add the white beans, basil pesto, olive oil, garlic powder, and a splash of the reserved pasta water. Toss everything together until well combined. If the mixture is too dry, add more pasta water as needed.
Season with salt and pepper to taste. Serve immediately, topped with grated Parmesan cheese if desired.