Step 1Heat the oven to 400 degrees. Butter an 8-or 9-inch cake pan with a removable bottom.
Step 2Place the butter, Dijon and dry mustards, salt and pepper in a small bowl and mash with a fork until creamy. Set aside.
Step 3Place the milk in a heavy saucepan and heat it until bubbles form around the sides. Add the butter mixture and bring to a rolling boil. Add the flour all at once, stirring vigorously until the mixture forms a ball and leaves the sides of the pan clean.
Step 4Transfer the dough to the bowl of an electric mixer and add one egg at a time, blending well after each addition, until the dough is shiny and smooth.
Step 5Stir in 1 cup of the cheese and blend well. Place the dough in a pastry bag fitted with a 1/2-inch tube. Pipe half the dough in slightly overlapping ovals to the center of the pan. Repeat one more layer on top until all the dough is used. Sprinkle the top with 1 tablespoon of cheese and brush with milk. Bake until puffed and golden brown, 35 to 45 minutes. Keep an eye on the souffle so it doesn't become too browned. Serve immediately.