Preheat oven to 400°F (200°C) and lightly grease a 9-inch (23 cm) baking dish.
Trim and cut broccoli into medium florets; rinse and drain thoroughly.
Bring a large pot of salted water to a boil; blanch broccoli 2 minutes until bright green.
Transfer broccoli to an ice bath to stop cooking, then drain and pat dry.
Melt butter in a saucepan over medium heat until foaming.
Whisk in flour and cook 1 minute to form a roux without browning.
Gradually whisk in milk and cream, simmer until sauce thickens to coat the back of a spoon.
Stir in Dijon mustard, nutmeg, half the cheddar, and Parmesan; season with salt and pepper.
Arrange broccoli in the prepared dish and pour the cheese sauce evenly over the florets.
Sprinkle remaining cheddar and optional breadcrumbs (tossed with olive oil) over the top.
Bake uncovered 12–15 minutes until sauce bubbles and cheese melts; broil 1–3 minutes if needed for a golden top.
Remove from oven and let rest 5 minutes before serving to allow the sauce to set.