Preheat oven to 350 degrees F (175 degrees C). Grease an 8-inch springform pan with 1 teaspoon butter. Dust with 1 teaspoon flour, shaking out excess.
Combine milk, 1 cup flour, eggs, Parmesan cheese, 1 tablespoon oil, baking powder, and nutmeg in a blender; blend until batter is smooth, about 1 minute. Pour into prepared pan.
Heat 2 tablespoons oil and 1 tablespoon butter in a large skillet over medium heat until butter is melted. Add leeks, fennel, and salt; cook and stir until softened, about 2 minutes. Spoon over batter in the pan. Arrange Brie cheese on top.
Bake in the preheated oven until center is firm and edges start to brown, 18 to 20 minutes. Let cool in the pan, 10 minutes. Run a knife around the edge of the pan to loosen edges and release the sides. Cut into slices.