Step 1

Place a rack in middle of oven; preheat to 350°. Coat a 13x9" pan with nonstick spray. Dust with flour, tapping out any excess.

Step 2

Whisk baking powder, cinnamon, salt, and 2 cups flour in a medium bowl until combined.

Step 3

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.

Step 4

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.

Step 5

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.

Step 6

Whisk condensed milk, coconut milk, cream, rum, lime zest, and salt in a medium bowl until combined.

Step 7

Using a skewer, poke holes every ½" 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.

Step 8

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.

Step 9

Spread rummy whipped cream evenly over cooled cake. Top with coconut chips.

Step 10

Do Ahead: Cake can be baked and soaked 1 day ahead. Let cool, then cover and chill. Top with rummy whipped cream and coconut chips just before serving.