With the rack in the middle position, preheat the oven to 400°F (200°C). Butter a 9 x 5-inch (23 x 13 cm), 6-cup (1.5 litre) loaf pan.
In a pot over medium heat, melt the butter. Add the flour and cook for 1 minute while whisking. Add the milk while whisking. Bring to a boil. Simmer gently for 2 minutes or until the béchamel sauce thickens. Stir in the cheese and cook just until completely melted. Season with salt and pepper.
Using an electric mixer, beat the eggs for 5 minutes or until frothy doubled in volume. With the machine running on high, add the béchamel sauce. Adjust the seasoning.
Pour into the loaf pan and bake for 30 to 35 minutes or until the omelette puffs up and is cooked through at the centre. Serve immediately.
You can prepare the béchamel sauce in advance and keep refrigerated. Simply reheat it in the microwave oven before adding to the beaten eggs. This recipe also cooks well in an enamelled cast iron pan.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.