Cake

Nonstick vegetable oil spray
2 cups all-purpose flour, plus more for pan
1 Tbsp. baking powder
1/2 tsp. kosher salt
4 large eggs
1 1/3 cups granulated sugar
2 Tbsp. dark rum
3/4 cup unsweetened coconut milk, divided

3-Milk Rum Soak

1 14-oz. can sweetened condensed milk
1 cup unsweetened coconut milk
3/4vcup heavy cream
1/4 cup dark rum
1 tsp. finely grated lime zest
1/4 tsp. kosher salt

Rummy Whipped Cream and Assembly

1 1/4 cups heavy cream
1/4 cup powdered sugar
2 Tbsp. dark rum
1 tsp. finely grated lime zest
Pinch of kosher salt
1 cup toasted coconut chips

Cake

Place a rack in middle of oven; preheat to 350°.
Coat a 13x9" pan with nonstick spray.
Dust with flour, tapping out any excess.
Whisk baking powder, cinnamon, salt, and 2 cups flour in a medium bowl until combined.
Beat eggs, granulated sugar and rum in the bowl of a stand mixer fitted with the whisk attachment at medium-high speed until pale yellow, doubled in volume, and mixture falls off whisk in a thick ribbon, about 5 minutes.
Fold in half of dry ingredients with a rubber spatula until most of the flour is incorporated.
Fold in half of coconut milk until just absorbed and no more streaks of flour remain.
Repeat with remaining dry ingredients and coconut milk.
Pour batter into prepared pan.
Tap gently against counter to spread and pop any bubbles.
Bake cake until top is set and golden brown and a tester inserted into the center comes out clean, 35–40 minutes.

3-Milk Rum Soak

Whisk condensed milk, coconut milk, cream, rum, lime zest, and salt in a medium bowl until combined.
Using a skewer, poke holes every ˝" into hot cake as soon as it comes out of the oven, wiggling the skewer to gently widen the holes and reach bottom of cake.
Slowly pour milk mixture over cake a spoonful at a time, letting it fully absorb before adding the next.
Be patient and don’t rush. At times it will look like too much milk, but it will all soak in.
Transfer pan to a wire rack and let cake cool completely, about 2 hours.

Rummy Whipped Cream and Assembly

Beat cream in bowl of stand mixer fitted with the whisk attachment until soft peaks form, 3–4 minutes.
Add powdered sugar, rum, lime zest, and salt and continue to beat until stiff peaks form, 1–2 minutes.
Spread rummy whipped cream evenly over cooled cake.
Top with coconut chips.