In a small mixing bowl, combine the softened mascarpone cheese, powdered sugar, vanilla extract, and ground cinnamon. Stir gently until smooth and well combined.
Spread the mascarpone mixture evenly onto two slices of bread, leaving a small border around the edges. Place the remaining slices of bread on top to form two sandwiches.
In a shallow dish, whisk together the eggs and whole milk until fully blended. Dip each stuffed sandwich into the egg mixture, allowing it to soak for about 30 seconds per side until the bread is fully coated but not soggy.
Heat a large nonstick skillet over medium heat and add 1 tablespoon of unsalted butter. Once the butter has melted and begins to bubble, carefully place the sandwiches in the skillet.
Cook the sandwiches for 3 to 4 minutes on each side, or until golden brown and crispy. Add more butter to the skillet if needed to prevent sticking.
Remove the French toast from the skillet and let it rest for 1 minute on a wire rack or plate. Slice diagonally and serve warm.