Bahamian Rum Cake

CAKE:
3 cups (420 g) AP flour
1/2 tsp baking powder
1/2 tsp baking soda
3/4 tsp salt
1/4 tsp freshly grated nutmeg
1 c (8 oz/225 g) unsalted butter, at room temp
2 c (400 g) granulated sugar
3 large eggs, at room temp
2 large egg yolks, at room temp
1 Tbsp vanilla extract
3/4 c (180 mL) canned Thai coconut milk

COCONUT-RUM SYRUP
3/4 c (180 mL) canned Thai coconut milk
6 Tbsp (75 g) granulated sugar
1/2 (125 mL) dark rum

GLAZE
4 Tbsp (2 oz/60 oz) unsalted/salted butter cut into pieces
6 Tbsp (90 mL) heavy cream
6 Tbsp (90 g) dark brown sugar
Pinch of salt
1 Tbsp dark rum
(1/2 c) 40 g dried large-flake coconut, toasted

DIRECTIONS
Preheat oven to 350F. Coat a 10-c Bundt cake or Tube pan with butter/nonstick cooking spray, dust it with flour, tap out the extra.
To make the cake, into a medium bowl, sift together the flour, baking powder, baking soda, 3/4 tsp salt, and the nutmeg.
In a stand mixer fitted with the paddle attacchment, beat together the 1 cup butter and 2 c granulated sugar on medium speed until light and fluffy, 3 to 5 minutes.
In a small bowl, beat together the egg, egg yolks, and vanilla. With the mixer running, slowly dribble the egg mixture into the butter mixture, stopping the mixer and scraping down the sides of the bowl as needed, until the eggs are completely incorporated (The mixture may look curdled, which is normal). Gently stir in 1/3 of the flour mixture, then about half of the 3/4 cup coconut milk. Mix in about half the remaining flour mixture, followed by the remaining coconut milk. Finally, gently stir in the remaining flour mixture just until combined.
Scrape the batter into the prepared pan and bake until the cake feels just set in the center, 55-60 minutes.
While the cake is baking, make the coconut-rum syrup. In a medium saucepan, warm the 3/4 cup (180 mL) coconut milk and the 6 Tbsp (75 g) granulated sugar, stirring until the sugar dissolves. Remove from the heat and add the 1/2 cup (125 mL) rum.
When the cake comes out of the oven, leave it in the pan and poke it with a wooden skewer about 60 times. Spoon 2/3 of the coconut-rum syrup over the cake, letting it soak in gradually. Let the cake cool completely.
Invert the cake onto a cake plate. Brush/spoon teh remaining coconut-rum syrup over the cake.
To make the glaze, in a small saucepan over high heat, bring the 4 Tbsp butter, the cream, brown sugar, anda pinch of salt to a boil. Cook, stirring to dissolve the sugar, for 1.5 minutes. Remove from the heat, stir in the 1 Tbsp rum, and let cool completely. Once cool, stir in the toasted coconut.
Spoon the glaze over the top of the cake, encouraging it to run down the sides of the cake (if the glaze seems too thick, rewarm it slightly).

STORAGE: The cake can be stored at room temperature for up to 4 days, preferably under a cake dome.