Preheat the oven to 350 degrees F (175 degrees C). Spray a 2-quart baking dish with nonstick spray.

Whisk milk, eggs, milk, and salt together in a bowl.

Place about 3/4 of the bread cubes into the prepared baking dish and sprinkle with ham and 1 cup Cheddar cheese. Carefully pour egg mixture over top. Add remaining bread cubes and gently press all over to submerge into the liquid. Once all of the bread is coated by the egg mixture, sprinkle remaining Cheddar cheese over the top.

Bake in the preheated oven until light golden brown and set in the middle, about 40 minutes. Allow to cool for 10 minutes before slicing and serving.