With the rack in the middle position, preheat the oven to 180°C (350°F).
In a bowl, combine the flour and baking powder. Add the equivalent of 1 egg, whisking until the mixture is smooth. Add the remaining eggs and the milk. Season with salt and pepper. Set aside.
Pour the fat into a hot cast iron skillet and add the egg mixture. Stir to combine. Transfer to the oven and bake until the omelet is golden and slightly puffy. Serve immediately. (The omelet will start to collapse after about 3 minutes.)
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.