Prep: Preheat oven to 350°F (175°C). Grease pans and line with parchment paper.
Mix Dry: Whisk flour, baking powder, baking soda, and salt in a bowl.
Cream Fats: Beat butter, oil, and brown sugar until fluffy (3 mins).
Add Wet: Beat in eggs one at a time, then vanilla.
Combine: Alternate adding flour mix and buttermilk to the wet bowl. Mix just until combined.
Bake: Pour into pans. Bake 25–30 mins. Cool completely.
Make Caramel: Melt sugar in a saucepan over medium heat until amber. Whisk in butter (careful, bubbles!). Remove from heat. Whisk in cream and salt. Cool.
Make Frosting: Beat butter until pale. Add powdered sugar and ½ cup cooled caramel. Whip until fluffy.
Assemble: Frost the layers. Pour remaining caramel over the top for a drip effect. Top with sea salt.