Preheat oven to 350°F (175°C). Grease and line cake pans with parchment.
Whisk flour, baking powder, and salt in a bowl. Set aside.
Cream butter and brown sugar until fluffy. Add eggs one at a time, then vanilla.
Alternate adding dry ingredients and milk, mixing until smooth.
Divide batter evenly into pans. Bake 30–35 minutes (toothpick test). Cool completely.
Melt butter in a saucepan over medium heat. Add brown sugar and cream; boil 2 minutes.
Remove from heat, stir in vanilla and salt. Gradually mix in powdered sugar until smooth.
Cool slightly (frosting will thicken as it cools).
Level cake layers if needed. Spread frosting between layers and over the top/sides.
Optional: Drizzle extra caramel sauce on top.