Preheat oven to 425°F with rack in middle. Butter 10-inch glass pie plate or round casserole dish, then sprinkle the pan with bread crumbs.
Heat a small saucepan over medium-high heat, and add the oil. Cook shallots until softened, about 5 minutes. Spread in dish, then evenly sprinkle cheese on top.
In a separate bowl, whisk together eggs, milk, crab, and pepper, and pour over cheese. Bake until top is golden and custard is set in center, 20 to 25 minutes for a shallow pan, and 30-40 minutes for a deep pan. Allow baked frittata to cool 10 minutes before serving. Cut into wedges to serve. Enjoy!
Can be served hot, at room temperature, or cold from the fridge.