INGREDIENTS
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Vegetable-oil cooking spray, for pans
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3 3/4 cups all-purpose flour
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1 1/4 teaspoons baking powder
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3/4 teaspoon baking soda
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2 1/2 teaspoons coarse salt
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10 ounces (2 1/2 sticks) unsalted butter, softened
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2 1/2 cups packed dark-brown sugar
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4 large eggs, room temperature
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1 tablespoon plus 1 teaspoon pure vanilla extract
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1 1/4 teaspoons rum, preferably golden or dark
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1 1/4 cups buttermilk, room temperature
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12 ounces unsalted butter (3 sticks), 1 stick left whole, 2 sticks cut into small pieces, softened
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2 cups packed dark-brown sugar
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1 cup heavy cream
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1/2 teaspoon coarse salt
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20 ounces cream cheese, softened
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1/2 cup confectioners' sugar, sifted
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2/3 cup packed dark-brown sugar
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3 ounces (6 tablespoons) butter, cut into pieces
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1/2 cup light corn syrup
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1/4 teaspoon coarse salt
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1/2 cup heavy cream
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2 cups pecan halves, toasted and chopped, plus more halves for garnish