Preheat oven to 350 degrees F. Lightly grease a 9-inch pie pan.
Heat oil in a large skillet over medium-high heat. Add onions and cook, stirring occasionally, until soft, about 3 minutes. Stir in spinach and continue to cook until excess moisture has evaporated.
Whisk together eggs, salt, and pepper in a large bowl. Add Muenster cheese and spinach mixture and stir until well blended.
Pour into the prepared pan.
Bake in the preheated oven until eggs have set, about 30 minutes.
Remove from the oven and let cool for 10 minutes before serving.