Gently cut brioche into 4 slices (about 1 to 1.5 inches thick) with a long serrated knife.
Use a paring knife to create a “pocket” in the brioche for stuffing with Nutella. First, take one slice of brioche and insert the knife along the bottom edge about 1 inch from the corner. Press the knife about halfway to two-thirds into the slice of brioche, then gently saw back and forth to cut a slit along the bottom edge of the bread. Stop about 1 inch from the other corner and remove the knife. Repeat with the remaining brioche slices.
Next, stuff the brioche with Nutella. Start by scooping about 1 tsp of Nutella onto a butter knife. Then, carefully open the pocket you made in one slice of brioche and fully insert the knife at the center of the pocket. Gently press down on the top of the brioche and rock the knife back and forth inside the pocket (like a pendulum motion), and remove the knife.* Repeat with the remaining brioche slices.
Now prepare your egg wash. Whisk egg, milk, cinnamon, and nutmeg in a large, shallow dish until combined.
Melt 1 tsp butter over medium heat on a griddle or large skillet. Gently coat both sides of the brioche in the egg mixture, one slice at a time, and transfer to the griddle.
Cook until the bottoms are lightly browned, about 3 to 4 minutes, checking periodically with a spatula. Flip the slices over and cook again until lightly browned, about 3 to 4 more minutes.
Plate two pieces of French toast per person. Optionally top with butter, maple syrup, a sprinkle of powdered sugar, and a dollop of whipped cream. Serve immediately.