Preheat oven to 375°F.
Blend butter with brown sugar until well combined. Spread the mixture generously over one side of each slice of bread; sandwich the slices. Halve sandwiches diagonally.
Arrange sandwich halves, single point side up, in a greased 9-inch square or 11 x 7-inch baking dish. Whisk together eggs, cream, corn syrup and vanilla until combined. Pour evenly over bread, spooning the egg mixture over each piece to coat bread evenly. Cover and refrigerate for at least 2 hours or overnight.
Cover and bake for 40 minutes. Uncover and bake for 10 minutes longer or until browned.