Preheat oven broiler.
In a small bowl, combine first 8 ingredients (oil through black pepper); divide mixture in half.
Evenly season flounder with salt and pepper, to taste, and arrange on a lightly oiled baking pan; broil until opaque throughout (8 to 10 minutes).
Meanwhile, steam broccoli florets till tender-crisp; drain then toss with half of the mustard sauce; arrange evenly on dinner plates.
Top each with flounder fillet and garnish with remaining mustard sauce.