Steam the broccoli until tender, or cook it in the tortellini boiling water for the last 2–3 minutes; drain both, reserving 1/4 cup of the tortellini cooking liquid before draining.
While the pasta cooks, melt the butter in a large skillet over medium heat, then add the chopped onion and cook about 2 minutes until softened.
Add the minced garlic, red pepper flakes, and a pinch of nutmeg; cook 1–2 minutes until fragrant but not browned.
Pour in the half-and-half and bring to a gentle simmer; simmer 2–3 minutes to slightly reduce and warm through.
Reduce heat to low and stir in the grated Parmesan until melted and smooth.
Add the drained tortellini, broccoli, and the reserved 1/4 cup pasta cooking liquid to the sauce; stir to combine and cook a few minutes until the sauce thickens and coats the pasta.
Season to taste with salt and pepper and serve with extra Parmesan if desired.
