Preheat the oven to 350 degrees . Grease a 2-quart baking dish. Layer the bread, ham, 2 cups cheese and 2 tablespoons chives in the dish. In a medium bowl, whisk together the eggs, milk, 1/4 teaspoon salt and 1/2 teaspoon pepper. Pour into the dish and top with the tomato slices in an even layer.
Bake the eggs until nearly set, about 30 minutes. Sprinkle the remaining 1/2 cup cheese and 1 tablespoon chives on top and bake until golden.