In sauté pan, lightly sauté onions, celery in the vegetable oil, just until soft. Let cool approximately 10-15 minutes.
Stir together corned beef, sautéed vegetables, egg. Set aside.
In same sauté pan, melt butter. Stir in flour and stir constantly for 1 minute. Add milk to make roux; cook until thickened. Season with ground black pepper. Remove from heat and stir into meat mixture.
Place in greased 8x8-inch baking dish.
Mix bread crumbs with 3 tablespoons melted butter and sprinkle over the top of corned beef mixture.