Slice bread into ½-inch slices, and let sit out while you prepare the rum sauce.
To make the rum sauce, add the butter to a medium saucepan over medium-low until melted. Add brown sugar, 1 teaspoon vanilla extract, 1 teaspoon cinnamon, ½ teaspoon nutmeg, ¼ teaspoon cloves, and rum; whisk to combine. Simmer over medium-low heat for 10-12 minutes, stirring occasionally, until the sauce thickens to the consistency of maple syrup.
Grease the bottom and sides of 9x13 inch baking dish with butter. Pour half of rum sauce into an even layer in the bottom of the pan.
In a large bowl, whisk together eggs, milk, 1 teaspoon vanilla extract, 1 teaspoon cinnamon, ¼ teaspoon nutmeg, and ¼ teaspoon cloves. Submerge bread slices into egg mixture and press gently to absorb the liquid. Arrange slices into baking dish by standing them at an angle. Once all bread slices are soaked and in the baking dish, pour any remaining egg mixture over the bread slices and drizzle with remaining rum sauce.
Cover and place in the fridge for one hour or overnight. When ready to bake, preheat the oven to 350° F. Bake uncovered for 55-60 minutes. If the bread begins to brown too quickly, cover with foil for the remainder of the baking time.
Slice and serve warm with maple syrup, whipped cream, and berries!