In a medium bowl, beat the softened cream cheese with granulated sugar and vanilla extract until smooth and spreadable, about 1 minute.
Using a sharp paring knife, carefully cut a horizontal pocket into the side of each bread slice, creating an opening about 2 inches wide without cutting all the way through to the edges.
Spread about 2 tablespoons of the cream cheese mixture into each bread pocket, distributing it evenly. Gently press the edges together to seal.
In a shallow dish, whisk together the eggs, milk, cinnamon, and salt until fully combined and no streaks of egg white remain.
Heat a large skillet or griddle over medium heat and add 1 tablespoon of butter, swirling to coat the surface.
Working with 2-3 slices at a time, quickly dip each stuffed bread slice into the egg mixture for about 3 seconds per side, allowing excess to drip off.
Place the coated slices in the hot skillet and cook for 3-4 minutes per side, until deep golden brown and the custard is set. The cream cheese should be warm and slightly melted inside.
Transfer cooked slices to a serving platter and repeat with remaining bread, adding more butter to the pan as needed.
Dust with powdered sugar and serve immediately with maple syrup on the side.
