Line a 20-cm (8-inch) square baking pan with plastic wrap.
In a saucepan, melt the butter. Add the flour and cook for 1 minute over medium heat, stirring constantly. Gradually whisk in the milk and bring to a boil over medium heat, stirring constantly. Add the Parmesan and Gruyère cheese. Stir until the cheese has melted. Add the mascarpone and egg yolk and stir to combine. Season with salt and pepper.
Pour the mixture into the prepared pan. Cover with plastic wrap and press with a spatula to smooth out the surface. Refrigerate for at least 4 hours or until the mixture is firm. Remove from the pan and cut into 36 cubes.
Place the flour in a shallow plate, the eggs in a bowl and the breadcrumbs in a second bowl.
Dip each cheese cube in the flour, and then dip it in the egg and the breadcrumbs. Place on a baking sheet.
In a deep skillet, pour the oil, about 5-cm (2-inch) high. Heat the oil over medium heat. Fry the cubes for 1 to 2 minutes on each side.
Serve as an appetizer or main dish with a green salad.
Although the fondue parmesan squares cook well in a skillet, for perfect and consistent colour, use a deep fryer.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.