1 cup coarsely grated Cheddar cheese (about 4 ounces)
Preheat the oven to 450°. In a large bowl, whisk the eggs with the milk, salt and pepper. Stir in the bread until evenly moistened, then stir in the ham, Gouda cheese, sun-dried tomatoes and 1/4 cup of the chives.
Butter a 9-by-12-inch baking dish and pour in the strata mixture. Sprinkle the Cheddar cheese on top. Bake for about 20 minutes, until puffed and golden. Let cool slightly, sprinkle with the remaining chives and serve.