In a shallow wide bowl, whisk together the liquid egg whites, whole egg, ground cinnamon, vanilla extract, and sea salt until the mixture is uniform and frothy.
Place the brioche slices into the egg mixture and let them soak for at least 2 minutes per side, ensuring the bread absorbs as much of the protein-rich custard as possible.
Heat a large non-stick skillet over medium-low heat and add the ghee, swirling the pan to ensure the surface is completely coated.
Carefully place the soaked brioche slices into the skillet and cook for 4 to 5 minutes on the first side until a deep golden-brown crust forms.
Flip the slices and cook for another 3 to 4 minutes, or until the center is set and the exterior is beautifully caramelized.
While the toast finishes, stir the Greek yogurt in a small bowl until it reaches a smooth, spreadable consistency.
Transfer the French toast to a plate, top with a generous dollop of Greek yogurt, scatter the fresh raspberries over the top, and finish with a drizzle of maple syrup.