1. Butter bottom and sides of a 9-by-13-inch baking dish. Make a deep slit in each bread slice to create a pocket. Stuff each with 1 slice of ham, then divide cheese evenly among pockets.

2. Whisk together eggs and milk in a bowl until combined, and season with salt and pepper. Pour egg mixture into prepared baking dish. Add bread slices in a single layer, gently pressing into egg mixture, and let soak 15 minutes. Flip bread You can soak the bread in the egg mixture for just 30 minutes, but the French toast will be even more delicious if you let it sit overnight. and gently press again into egg mixture. Let soak 15 minutes. (If preparing the day before, refrigerate up to 12 hours, loosely covered, then let stand at room temperature 30 minutes.)

3. Preheat oven to 350 degrees. Top bread with remaining ham and cheese. Bake until egg mixture is set and cheese is melted, 20 to 25 minutes.

4. Turn oven to broil, with rack 4 to 6 inches from heat source. Broil until bread is toasted and golden brown, 1 to 2 minutes. Serve hot with maple syrup.