In a large, shallow baking dish, vigorously whisk together the 4 large eggs, 1 cup of whole milk, 2 tablespoons of granulated sugar, 1 teaspoon of ground cinnamon, 1 teaspoon of vanilla extract, and 1/4 teaspoon of salt until the mixture is completely smooth and uniform in color.
Preheat a large non-stick skillet or griddle over medium-low heat and add 1 tablespoon of the unsalted butter, allowing it to melt and coat the surface.
Dip one slice of Brioche bread into the egg mixture, letting it soak for about 20-30 seconds per side until the bread is fully saturated but not falling apart.
Place the soaked bread slice onto the preheated skillet and cook for 3-4 minutes, or until the bottom is golden brown and crisp.
Carefully flip the French toast with a spatula and cook the other side for another 3-4 minutes until it is also golden brown and the center is cooked through.
Transfer the cooked French toast to a baking sheet and keep warm in a 200°F oven. Repeat the dipping and cooking process with the remaining bread slices, adding the second tablespoon of butter to the skillet as needed.