Combine 2 cups flour, yeast, sugar, and salt in the bowl of a stand mixer fitted with the paddle attachment.
Combine milk and margarine in a 1-quart saucepan; heat over low heat until milk is very warm and margarine is mostly melted, about 5 minutes.
Beat milk mixture into the flour mixture on low speed until just combined. Increase speed to medium and beat until smooth, about 2 minutes. Add remaining 2 cups flour; beat until a soft dough forms. Switch to the dough hook and knead until smooth and elastic, about 10 minutes.
Transfer dough to a greased bowl. Turn over to coat. Cover and let rise until doubled, about 1 hour.
Gently punch down dough to deflate. Let rise until doubled again, about 45 minutes.
Preheat oven to 375 degrees F (190 degrees C). Grease a 9-inch round baking pan.
Gently punch down dough and roll into a circular shape. Transfer to the baking pan.
Mix Muenster cheese, egg, and egg yolk together in a bowl. Spread over dough in the baking pan. Gather up dough in 1 1/2-inch pleats. Squeeze pleats together gently and twist to make a topknot.
Let dough rest, 10 to 15 minutes. Brush with egg white.
Bake in the preheated oven until golden brown, about 1 hour.