Place eggs in a saucepan and cover with water. Bring to a boil, remove from heat, and let eggs stand in hot water for 15 minutes. Remove eggs from hot water, cool under cold running water, and peel.
Chop eggs and transfer to a large bowl.
Stir mayonnaise, Dijon mustard, sweet pickle relish, steak sauce, paprika, and dill into eggs until well mixed; season with salt and black pepper. Cover and refrigerate until chilled, if desired.
