Combine the egg with the milk, sugar, cinnamon, vanilla, and salt in a bowl; whisk until well blended.
Dip each slice of bread in the egg batter, then place them on a foil-lined baking sheet.
Melt about 1 teaspoon of butter in a large skillet or griddle over medium-low heat until sizzling. Place 2 battered slices of bread in the pan and cook until browned on the bottom, about 2 minutes. Flip the bread over and brown the other side for about 2 minutes longer.
Repeat with the remaining butter and bread slices.