Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans, ensuring even coverage to prevent sticking. Combine the sour cream and milk in a small bowl, stirring until smooth. Set aside.

In a large mixing bowl, beat the softened butter on medium speed using a stand mixer or hand mixer until creamy. Gradually add the granulated sugar, continuing to beat until the mixture is light and fluffy. This process typically takes 3 to 4 minutes.

Add the eggs one at a time, mixing well after each addition. Ensure each egg is fully incorporated before proceeding to the next to create a smooth batter.

In a separate bowl, whisk together the all-purpose flour, baking powder, and salt. These dry ingredients will provide structure and ensure even distribution of the leavening agent.

Gradually add the dry ingredients to the butter mixture, alternating with the sour cream mixture. Begin and end with the dry ingredients, mixing on medium-low speed after each addition. Stir in the vanilla extract and rum extract until just combined.

Divide the batter evenly between the prepared pans. Bake in the preheated oven for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean. Allow the cakes to cool in the pans on a wire rack for 10 minutes before removing them. Transfer the cakes to the wire rack to cool completely, approximately 2 hours.

Once the cake layers are fully cooled, spread a generous layer of caramel frosting between the layers, then frost the top and sides. Smooth the frosting for a polished appearance, or leave it slightly rustic for a homemade feel.