Heat the oven to 375°F and grease a 9-by-13-inch dish. Blanch the broccoli for 2 minutes, drain and dry well.
Brown the beef and onion in a skillet and drain. Transfer to a bowl with the broccoli and rice.
Melt the butter in the skillet, stir in the flour for 1 minute, then whisk in milk, Dijon, salt and pepper and simmer until thickened.
Remove from heat, stir in 2 cups cheddar, and fold the sauce into the beef mixture. Spread in the dish and top with remaining cheese.
Bake for 25 to 30 minutes, until bubbling. Rest for 10 minutes.