Toss the broccoli with the oil and pinch of salt and pepper, lay on a baking sheet, and roast until tender and lightly charred, about 20-30 minutes. Remove from oven and turn heat down to 375.
Make the sauce. Melt the butter in a heavy pot, add the flour and cook for 3-4 minutes. Add mustard and nutmeg.
Whisk in the milk and the broth, and bring to a boil, continuously whisking.
Turn off heat and stir in the cheese.
Lightly butter a casserole dish and add the rice, sauce, and broccoli. Stir and sprinkle with cheddar and Parmigiano Reggiano.
Bake for 20-30 minutes, until cheese is bubbly. Let cool slightly before serving.