Preheat oven to 350°F and line 3 6-inch cake pans with parchment paper. Spray the lined pans with nonstick spray. Set aside.
In a medium bowl, whisk the flour, baking powder, and salt together. Set aside.
2¼ cups all-purpose flour, 2 teaspoons baking powder, ½ teaspoon kosher salt
In the bowl of a stand mixer fitted with the paddle attachment, beat the room temperature browned butter on medium speed until fluffy and light in color, about 1 minute.
1 cup browned butter
Add the brown sugar, allspice, cinnamon, and nutmeg. Beat on medium speed until light and fluffy, about 3 minutes.
1¾ cups dark brown sugar, 1 teaspoon ground allspice, 1 teaspoon ground cinnamon, 1 teaspoon ground nutmeg
Add the eggs, one at a time, mixing well after each addition. Add the dark rum and mix until combined. Use a spatula to scrape the sides of the bowl as needed.
4 large eggs, 1 tablespoon dark rum
With the mixer on low speed, alternate adding the dry ingredients and milk in batches to evenly incorporate: add ⅓ of the dry, ½ of the milk, ⅓ of the dry, last ½ of the milk, and last ⅓ of the dry. Scrape down the sides of the bowl to ensure that all of the ingredients are well mixed.
1 cup whole milk
Evenly divide the batter into the prepared pans (about 442 grams per pan).
Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Remove the cakes from the oven. Let the cakes cool in the pans for 10 minutes before removing from the pans and completely cooling on a cooling rack.