Preheat the oven to 425 degrees F. Bring a large pot of water to boil. Season the sole with salt and pepper. Roll the fillets up and place in a parchment-lined baking dish. Drizzle with the melted butter. Cover and bake 15 minutes, or until just cooked through.
While this occurs, place the milk and flour in a pot and whisk to combine. Set over medium heat and cook, stirring, until the mixture comes to a gentle simmer and the sauce thickens. Stir in the cheese, salt and pepper; then reserve over low heat.
When the fish is almost done, place the broccoli in the boiling water and cook 2 minutes.
Arrange the fish and broccoli on plates. Spoon the cheese sauce over the fish and serve.