Preheat oven to 425F with rack in middle.
Butter quiche dish, then sprinkle all over with bread crumbs.
Cook onions with ham in butter in a 12-inch heavy skillet over medium-high heat, stirring occasionally, until pale golden, about 5 minutes. Spread in dish, then evenly sprinkle cheese over the top.
Whisk together eggs, cream, milk, and ½ teaspoon pepper and pour over cheese. Bake until top is golden and custard is set in the center, 20 to 25 minutes. Cool slightly before cutting into wedges.