Steam the broccoli until tender, or add the broccoli to the tortellini pot for the last 2–3 minutes of cooking; cook tortellini according to package directions and reserve 1/4 cup of the pasta cooking liquid before draining.
In a large skillet over medium heat, melt the butter. Add the chopped onion and cook until softened, about 2 minutes.
Add the minced garlic, red pepper flakes, and a pinch of nutmeg; cook, stirring, for about 2 minutes until fragrant.
Pour in the half-and-half and bring the mixture to a gentle simmer; let it simmer for 2–3 minutes to slightly thicken.
Reduce heat to low and stir in the grated Parmesan until melted and the sauce is smooth.
Add the drained tortellini and cooked broccoli to the skillet along with up to 1/4 cup reserved pasta water; stir to combine and cook a few minutes more to thicken the sauce and heat through.
Season to taste with salt and pepper and serve with extra Parmesan if desired.