In a medium sized pot, brown the butter for the brioche recipe until it is lightly toasted. Let cool in the fridge for half an hour.
Mix brioche according to the standard directions, substituting your browned butter for the regular butter. Let rest in the refrigerator for 12 hours or overnight.
Shape chilled dough into 2-ounce rounds and place 2 inches apart on a baking sheet lined with parchment or a silicone mat.
Let proof at room temperature until the dough slowly springs back into place when touched lightly. Meanwhile, preheat the oven to 325°F.
When finished proofing, brush with the whisked egg and bake for 25 minutes, until golden brown.
After pulling from the oven, you can brush with additional brown butter and sprinkle with a finishing salt for the perfect final touch.