Dulce de Leche Cake

Preheat the oven to 350 degrees F (175 degrees C). Spray two 8-inch round cake pans with baking spray; set aside.

Whisk the flour with the baking powder and salt in a medium bowl until combined; set aside.

Add white sugar and butter to the bowl of a stand mixer fitted with a paddle attachment. Beat on medium-high until light and fluffy, 2 to 3 minutes. Add 1/3 cup dulce de leche and vanilla; beat until well combined, 30 seconds, scraping down sides of bowl as needed. Reduce speed to low and add eggs one at a time, beating until just blended after each addition, 45 seconds.

Add flour mixture alternately with 3/4 cup milk, beginning and ending with flour mixture and beating on low just until combined after each addition.

Evenly divide cake batter between prepared pans.

Bake in the preheated oven until golden and a toothpick inserted in the center comes out clean, 25 to 30 minutes. Cool cakes in pans for 10 minutes.

Prepare the glaze: Whisk together 1/4 cup dulce de leche and 2 tablespoons milk until mixture is smooth.

Invert cakes from pans onto a wire cooling rack; set rack on a baking sheet. Using a wooden skewer or fork, gently poke holes all over flat sides (bottoms) of cakes. Pour dulce de leche glaze mixture over cakes and smooth with an offset spatula to coax mixture into holes. Let cool completely, about 30 minutes.

Prepare frosting: Beat butter in a stand mixer fitted with the paddle attachment on medium speed until smooth, about 1 minute. With mixer running on low speed, gradually add powdered sugar, beating until smooth, about 1 minute, stopping to scrape down sides of bowl as needed. Beat in salt. Increase speed to medium, and beat until fluffy, about 2 minutes. Scrape down sides of bowl, and beat in 1/2 cup dulce de leche and rum (if using) on low speed until just incorporated, 45 seconds.

Assemble the cake: Set a cake layer on a plate with the flat side (bottom) facing up. Evenly spread 1 cup of the frosting over the cake to the edge. Sprinkle with 1/4 cup of hazelnuts. Top with the second cake layer, rounded (top) side up. Spread the remaining frosting over the top and side of the cake. Sprinkle with remaining 1/2 cup of hazelnuts on top.