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1
Position rack in middle of oven and preheat oven to 350 F. Spray Bundt pan with nonstick baking spray.
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2
Sift together flour, baking powder, baking soda, cinnamon, ginger, allspice, and 1/2 teaspoon salt; set aside. Combine cream and 3/4 cup rum in liquid measuring cup; set aside.
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3
With electric mixer fitted with paddle attachment beat 1 1/2 cups butter, 1 1/2 cups sugar, and lime zest on medium-high speed until light and fluffy, about 3 minutes. Add egg yolk and beat until fully incorporated. Add whole eggs, one at a time, beating well after each addition. Add vanilla and reduce speed to low.
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4
Add flour mixture in three additions, alternating with the cream-rum mixture, stopping once or twice to scrape the sides and bottom of bowl with a rubber spatula. Mix until smooth, about 20 seconds.
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5
Scrape batter into prepared pan and bake until a toothpick inserted into center of cake comes out clean, about 1 hour.
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6
Meanwhile, combine Coca-Cola, remaining 1/2 cup rum, and lime juice in liquid measuring cup; set aside.
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7
Place remaining 1 cup sugar and water in a heavy-bottomed, stainless steel, medium saucepan. Bring mixture to a boil over medium-high heat and cook, gently swirling saucepan from time to time, until the sugar turns deep amber and begins to smoke, 10 to 14 minutes.
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8
Immediately remove the saucepan from heat, and slowly and carefully pour in rum-and-Coke mixture. The mixture will sputter quite violently-don't move the saucepan or stir. Once the sputtering has subsided, return saucepan to medium heat, and, with a wooden spoon, stir until smooth, about 5 minutes. Stir in remaining 2 tablespoons butter and remaining 1/4 teaspoon salt. Reserve 1/2 cup glaze.
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9
Once cake is done, transfer to cooling rack. Poke it all over with a metal or wooden skewer. Pour glaze over the cake and allow it to sit in the pan for 20 minutes before turning out onto a cooling rack. Brush cake with reserved glaze and cool completely, about 1 hour. Serve.
