Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Drain and let cool slightly.
While the pasta cools, toast the pine nuts in a dry skillet over medium heat until golden and fragrant, about 2-3 minutes. Set aside.
In a blender or food processor, combine basil leaves, garlic, lemon juice, Parmesan, salt, black pepper, and olive oil. Pulse until a smooth paste forms. Add pine nut meal if using and blend for an extra 5 seconds.
Toss the cooled pasta with the pesto until fully coated. Add the cherry tomatoes, broccoli, red onion, and toasted pine nuts. Mix gently to combine.
Add the crumbled feta cheese and toss again. Chill in the refrigerator for at least 30 minutes before serving to let the flavors meld.
Serve cold or at room temperature, garnished with additional Parmesan or fresh basil if desired.