Heat the oven to 375°F and line a rimmed sheet pan with parchment. Cook onion in oil in a skillet over medium heat for 7 minutes, then spread on a plate to cool for 5 minutes.
Soak oats in milk for 10 minutes. Stir in eggs, cooled onion, Worcestershire, salt and pepper, then fold in beef just until evenly combined.
Shape into a 9-by-5-inch loaf about 2 1/2 inches high on the pan. Bake for 55 to 65 minutes until the center reaches 160°F.
Rest the loaf for 10 minutes. Melt butter in a saucepan over medium heat, whisk in flour and cook for 4 to 5 minutes until nut brown without black specks.
Gradually whisk in broth and mustard. Simmer for 5 to 7 minutes, stirring, until the gravy lightly coats a spoon.
Cut the rested loaf into 8 thick slices and spoon the hot gravy over them.