Whip the eggs together, then add the rest of the ingredients except for the bread. Gently combine in a wide, shallow bowl.
Dip the bread into the mixture; let each side sit 20-30 seconds. (We did four slices at a time.)
Heat a large flat skillet or griddle. Melt butter, 1 tbsp for each batch.
When butter is melted, swirl it around the pan to cover all surfaces.
Place slices of custard-covered Brioche bread into pan. Cook for 3-4 minutes per side, until gently browned and egg is no longer runny.
Flip bread and cook other side.
Stack toast until ready to serve with syrup, recipe below.