Prepare the filling. In a small bowl, mix the ground cinnamon, brown sugar, and softened butter until it forms a thick paste. Set aside.
Make the custard. In a medium bowl, whisk together the eggs, milk, vanilla, cinnamon, and a pinch of salt. You want a smooth, creamy mixture that will soak into the bread.
Assemble the sandwiches. Take a slice of bread and spread a spoonful of the cinnamon sugar filling on top. Place another slice on top to make a sandwich. Repeat with the rest of the bread.
Dip and cook. Preheat a large skillet or griddle over medium heat and lightly grease it with butter or oil. Dip each sandwich into the egg mixture, coating both sides well. Let the excess drip off, then place it in the hot skillet. Cook for about 2–3 minutes on each side or until golden brown and crisp.
Make the glaze. In a small bowl, whisk together the powdered sugar, cream cheese, milk, and vanilla until smooth and pourable.
Serve. Drizzle the warm glaze over the cooked French toast sandwiches and serve immediately.