01 - In a large pot, bring generously salted water to a rolling boil. Add the pasta and cook according to package directions. During the final 4 minutes of pasta cooking, add the broccoli florets to the same pot. Once cooked, drain the pasta and broccoli together, then set aside.
02 - In a large skillet, melt the unsalted butter over medium heat. Add the finely chopped onion and sauté for 2 to 3 minutes until it becomes translucent. Incorporate the minced garlic and cook for an additional minute, being careful not to burn it.
03 - Sprinkle the all-purpose flour into the skillet with the cooked onions and garlic. Whisk continuously for 1 minute to create a smooth roux.
04 - Gradually pour the whole milk into the roux, whisking constantly to prevent lumps. Add the heavy cream and bring the mixture to a gentle simmer. Continue to cook, stirring occasionally, until the sauce slightly thickens, which should take approximately 3 to 4 minutes.
05 - Stir in the grated Parmesan cheese, salt, ground black pepper, and the pinch of nutmeg (if desired). Continue stirring until the Parmesan is fully melted and the sauce achieves a smooth, creamy consistency.
06 - Add the drained pasta and cooked broccoli to the prepared sauce in the skillet. Toss thoroughly to ensure everything is evenly coated. If the sauce appears too thick, incorporate a splash of the reserved pasta water until the desired consistency is reached. Serve immediately.
07 - Garnish each serving with extra grated Parmesan cheese, freshly cracked black pepper, and chopped parsley, if desired, before enjoying.