In a large bowl, beat eggs with a whisk until light and frothy, about 2 minutes. Add milk, flour, and salt, and continue beating 3 to 5 minutes, until batter is smooth and creamy (it will be fairly thin).

Refrigerate batter overnight (see “Note”) or simply let it sit at room temperature 30 minutes. Fifteen minutes before you're ready to cook, preheat oven to 450° and set a rack to the middle position. Put a heavy-duty 10-inch ovenproof skillet in to preheat.

Remove the hot pan from the oven and add butter; tilt and swirl until melted and bubbly. Immediately pour batter into the hot pan and place in the oven. Bake until the edges are puffed and deep golden brown, about 20 minutes. Sprinkle ham and cheeses in the center and return to the oven until cheeses melt, 4 to 5 minutes. Remove from the oven, garnish with chopped chives, and serve immediately with maple syrup.