Boil the potatoes and carrots in salted water until tender, 30 to 40 minutes. Drain and mash or put through a food mill or potato ricer. Add the eggs, milk, butter, salt, and pepper, and mix well. Grease a 2-quart (2 L) baking dish and sprinkle half the bread crumbs on the bottom. Spoon the potato mixture into the baking dish and top with the remaining bread crumbs. Bake in a preheated 375F (190C) oven for 15 minutes.
Serves 6 to 8.
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