These tasty soldiers are meant to be eaten, then followed by a shot of sweetened rum -- they'll certainly keep the festivities going.
Preheat oven to 200 degrees. Whisk together eggs, milk, vanilla, and salt in a medium bowl; set aside.
Place bread in a shallow baking dish large enough to hold slices in a single layer. Pour egg mixture over bread; soak 5 minutes. Meanwhile, gently heat rum and syrup in a small pot over low heat until just warm.
Heat 1 tablespoon butter in a large nonstick skillet over medium heat. Fry 2 bread slices until golden brown, 3 to 4 minutes per side. Transfer to a wire rack set over a baking sheet and place in the oven to keep warm. Repeat, using remaining bread and butter.
Once all French toast has been cooked, slice into 3/4-inch-wide strips. Divide syrup among 12 shot glasses, and place 1 or 2 strips of French toast into each glass. Serve immediately.