Ice Cream French Toast

1 pint vanilla ice cream, melted
4 slices thick bread
5 tablespoons unsalted butter, divided

Preheat oven to 250°F. Pour ice cream into a large baking dish. Add bread, turn to coat, then let sit 3 minutes. Flip bread and continue to soak until saturated but not soggy, about 3 minutes more.
Heat 2 Tbsp. butter in a large skillet over medium. Using tongs, carefully lift 2 bread slices from custard, letting excess drip back into dish. Transfer to skillet in a single layer and cook until golden brown and the center of toast springs back when pressed, about 4 minutes per side. Transfer to a wire rack set inside a rimmed baking sheet; keep warm in oven until ready to serve. Repeat with 2 Tbsp. butter and remaining bread. Top toasts with remaining 1 Tbsp. butter and serve.