Dulce de Leche Layer Cake

Submerge the unopened can of condensed milk in a large, deep pot of water and bring to a boil. Simmer over moderately low heat for 2 hours, adding water as needed to keep the can completely submerged. Carefully remove the can and let cool slightly. Carefully open the can with tongs and transfer the dulce de leche to a bowl: It should resemble creamy caramel. Whisk until smooth, then gradually whisk in the nut liqueur. Let cool completely.

Preheat the oven to 350° and butter two 9-inch cake pans. Line with parchment paper and butter and flour the pans. In a medium bowl, whisk the flour with the baking powder and salt. In the bowl of a standing electric mixer fitted with the paddle, beat the butter with the 1 1/2 cups of sugar at medium speed until fluffy. Add the egg yolks and vanilla and beat until smooth. Beat in the dry ingredients and the milk in 3 alternating batches, scraping down the side of the bowl occasionally.

In a clean bowl, using clean beaters, beat the egg whites at medium-high speed until soft peaks form. Gradually add the remaining 6 tablespoons of sugar and beat until glossy. Fold the egg whites into the batter.

Scrape the batter into the prepared pans. Bake in the center of the oven for 40 to 45 minutes, until the cakes are golden and a toothpick in the centers comes out clean. Transfer the cakes to a rack to cool slightly. Run the tip of a knife around the edges and invert the cakes onto the rack to cool completely. Using a serrated knife, split each layer horizontally in half.

In a clean bowl, using clean beaters, beat the egg whites at medium-high speed until soft peaks form. In a medium saucepan, bring the sugar and water to a boil over high heat, stirring, until the sugar is dissolved and a candy thermometer in the syrup registers 235° for soft-ball stage. Remove from the heat and add the liqueur. With the mixer at medium speed, carefully drizzle the hot sugar syrup into the egg whites. Beat in the lime juice, then beat at high speed until the frosting is light and fluffy and slightly warm to the touch.

Place a cake layer on a large cake plate and top with one-third of the dulce de leche filling. Repeat with the remaining layers and filling, ending with a layer of cake. Spread the frosting all over the cake, swirling decoratively. Let stand at room temperature for at least 2 hours before serving.