Set a medium sautee pan over medium heat. Add the apples and fennel and cook until just softened. Remove from heat.
Roll out your dough into a 9-inch circle and transfer to a baking sheet. Arrange the apples and fennel on the center of the dough, leaving a border of at least 1 inch all the way around. Fold this border up and over, covering some of the filling. Bake for 30 minutes.
Meanwhile, melt butter in a small pan over medium heat. Add the onion and reduce heat to low. Cook, stirring frequently, until the onions become soft and golden – about 20 minutes.
Sprinkle the onions and cheese over the center of the galette and return to the oven. Bake an additional 10 minutes, or until cheese is melted and crust if fully cooked.