Make the cake batter: Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans. In a large bowl, cream the butter and sugar until light and fluffy. Add eggs one at a time, beating well after each. Stir in vanilla.

Mix the dry ingredients: In a separate bowl, whisk together flour, baking powder, and salt. Add to the wet ingredients alternately with the milk, beginning and ending with the flour mixture. Mix just until combined.

Bake the cakes: Divide the batter evenly between prepared pans. Bake for 28–32 minutes, or until a toothpick inserted in the center comes out clean. Cool in pans for 10 minutes, then transfer to a wire rack to cool completely.

Make the caramel frosting: In a saucepan over medium heat, melt butter. Stir in brown sugar and cook for 2–3 minutes, stirring constantly. Add milk and bring to a gentle boil. Remove from heat and let cool slightly. Gradually beat in powdered sugar, vanilla, and salt until smooth and spreadable.

Assemble the cake: Place one cake layer on a serving plate. Spread a thick layer of caramel frosting on top. Add the second cake layer and frost the top and sides with remaining caramel frosting.

Serve: Slice and serve at room temperature for the best texture and flavor.