Baba au Rhum Punch

Make the dough: In the bowl of a stand mixer fitted with a dough hook, stir together the milk, sugar, and yeast. Let stand until frothy, about 5 minutes. Add the flour and salt; beat on medium-low speed until the flour is mostly incorporated, about 1 minute, stopping to scrape down sides of bowl as needed. Beat in the eggs one at a time, then beat until the dough forms a slightly sticky ball, adding more flour a tablespoon at a time if the dough is too sticky, about 2 minutes. Add the butter; increase the speed to medium and beat until dough is smooth, elastic and no longer clings to the sides of the bowl, about 8 minutes. Cover the bowl with plastic wrap and let stand in a warm, draft-free place until the dough doubles in size, about 1 hour.

While dough rises, make the rum soak: In a small saucepan, bring the water, sugar, cinnamon sticks, and salt to a boil over medium-high heat, stirring until sugar dissolves. Remove the pan from the heat and stir in the lime juice, then the rum. Set aside to allow the cinnamon to infuse the rum soak, about 30 minutes.

Make the Coulis: In a medium saucepan, stir together the pureed fruit, sugar, lime juice, and lemon juice. Bring to a boil over medium heat; reduce to a simmer and cook, stirring often, until the coulis is viscous and coats the back of a spoon, 5 to 10 minutes. Strain the coulis through a fine-mesh sieve into a medium bowl. Add the rum and let cool to room temperature, about 40 minutes.

Preheat the oven to 375°F; lightly butter a 9½-inch Bundt pan. Punch down dough in bowl; remove from bowl and gently stretch into an approximately 18-inch length. Place the dough in the pan to form a wreath shape and press the top gently to flatten. Cover with a clean dishcloth. Set aside in a warm place and let rise until doubled in size, 20 to 30 minutes.

Bake until golden brown and a toothpick inserted into the center comes out clean or an instant-read thermometer inserted into the center of the cake reads 190°F to 200°F, 20 to 30 minutes.

Meanwhile, make the citrus glaze: In a small saucepan, whisk together the sugar and pectin. Whisk in the water and lemon juice until smooth; bring to a simmer over medium-high heat and cook until the mixture is pale and glue-like, 6 to 8 minutes.

Let the cake cool in the pan for 10 minutes. Invert the cake onto a wire rack set over a baking sheet. Using a cake tester, bamboo skewer, or cooking tweezers, gently pierce the cake all over (including the top, sides, and bottom). This will allow the syrup to soak in. Return the cake to the pan. Using the cake tester, gently pierce the top of the cake all over. Remove cinnamon sticks from the rum soak and slowly pour about half of the rum soak over the cake. Allow the soak to absorb into the cake. Invert the cake once more onto the wire rack and slowly pour the remaining rum soak over the cake.

Using a pastry brush, lightly coat the cooled, syrup-soaked baba with the glaze (you will have extra glaze left over).

To serve the baba au rhum, cut the cake into generous wedges and serve each slice with a scoop of ice cream and a drizzle of coulis.