Slice the brioche bread into thick pieces, about 1 inch each.
Place them on a baking sheet to dry out slightly, which helps absorb the custard better.
In a bowl, whisk together eggs, heavy cream, vanilla extract, sugar, and salt until well combined.
Make sure the mixture is smooth, with sugar thoroughly dissolved.
Dip each bread slice into the egg mixture for about 30 seconds on each side.
Allow the bread to soak up the liquid without getting too soggy.
Heat a non-stick skillet over medium heat and melt a bit of butter.
Place the soaked bread slices onto the skillet and cook until golden brown on one side, about 3 to 4 minutes.
Sprinkle a small amount of sugar on the uncooked side, then flip the bread.
Cook until the second side is golden and sugar has caramelized.