Heat the oven to 350°F (175°C). Grease a 9 x 13-inch baking pan with baking spray, or butter and flour it, and line it with parchment if desired.

Whisk the flour, baking powder, and fine salt together in a medium bowl. In a separate bowl, beat the softened butter and sugar for 3–4 minutes until pale and fluffy.

Beat in the eggs one at a time, then mix in the vanilla. Add the dry ingredients in three additions, alternating with the milk, and mix only until the batter is combined.

Spread the batter evenly in the prepared pan. Bake for 25–32 minutes, until the center springs back and a toothpick comes out clean or with a few moist crumbs.

Cool the cake in the pan for about 20–30 minutes. Use the handle of a wooden spoon or a large round straw to make holes approximately 1 inch apart across the cake.

For the caramel, combine the sugar and water in a heavy saucepan over medium heat. Stir only until the sugar dissolves, then let the syrup boil without stirring until it reaches a medium amber color.

Remove the caramel from the heat and carefully whisk in the butter. Slowly add the warm cream while whisking, remembering that the mixture will bubble vigorously, then stir in the sea salt.

Let the caramel cool for 10–15 minutes, then pour it over the holes in the cake. Spread any remaining caramel over the surface, and refrigerate the cake for at least 1 hour.

For the buttercream, beat the softened butter for 2–3 minutes until smooth. Gradually add the sifted confectioners’ sugar on low speed, then add the vanilla, fine salt, and cream.

Beat the frosting on medium-high speed for 3–5 minutes, until light and fluffy. Spread it over the chilled cake, drizzle with leftover caramel, and finish with a small pinch of flaky sea salt if desired.