Melt Butter: In a large skillet, melt butter over medium heat.
Make the Roux: Add flour to the butter and whisk for 1 minute.
Add Milk: Slowly add the milk while whisking, then simmer until the sauce thickens (about 5 minutes).
Add Beef: Stir in chopped beef and black pepper. Cook for an additional 2 minutes until heated through.
Serve: Spoon over toasted bread and enjoy!