Bring a large pot of salted water to boil. Add the broccoli florets to the boiling water for about 2 to 3 minutes, until fork-tender. Remove with a slotted spoon.
In the same pot, add the short cut pasta and cook according to package instructions, about 7 to 10 minutes until al dente. Drain the pasta.
In a skillet over medium heat, add the olive oil, diced onion, and sauté for about 5 minutes until browned and softened. Then add the minced garlic and cook for an additional minute.
In a food processor, combine the sautéed onion and garlic, broccoli florets, grated parmesan cheese, and a splash of reserved pasta water. Pulse until it starts to come together, adjusting with more pasta water or heavy cream for desired consistency.
Toss the drained pasta with the broccoli pesto sauce, ensuring all pasta is well coated. Taste and adjust seasoning with salt and pepper.
Serve warm, topped with more grated parmesan cheese if desired.
