Preheat oven to 350°F. Lightly grease or butter a 1-quart casserole dish.

Whisk together egg, parsley, mustard, salt, and pepper.

Melt 3 tablespoons butter in a medium sauce pan over medium heat. Add 1/2 cup breadcrumbs and half-and-half. Cook until slightly thickened, stirring constantly.

Remove from heat and add egg mixture, stirring rapidly while adding so the egg is incorporated in without cooking/scrambling in the pan.

Stir in crabmeat. Pour mixture into prepared casserole dish and spread evenly in the dish.

Melt remaining 1 tablespoon butter and stir in remaining 1/4 cup breadcrumbs. Sprinkle evenly over casserole.

Bake for 25 minutes.