Grease a 9x13-inch baking pan.

Stir brown sugar, melted butter, and cinnamon together in a small bowl; spread into the prepared pan. Spread apple pie filling evenly over top, then layer on bread slices, pressing down as you go.

Beat milk, eggs, and vanilla together in a bowl; slowly pour over bread, making sure egg mixture is completely absorbed. Cover pan with aluminum foil; refrigerate 8 hours to overnight.

Preheat the oven to 350 degrees F (175 degrees C).

Bake in the preheated oven, covered, for 1 to 1 1/4 hours. Turn on the broiler. Uncover pan; drizzle maple syrup on top. Broil until syrup begins to caramelize, 2 minutes. Remove from oven; let stand for 10 minutes, then cut into squares. Invert pan onto a serving tray or baking sheet so apple filling is on top. Serve hot.