Heat the oven to 350°F (175°C). Grease two 9-inch round cake pans, line the bottoms with parchment, and lightly flour the sides.

Whisk together the flour, baking powder, and salt. In a separate bowl, cream the softened butter and granulated sugar for 3–5 minutes, until pale and fluffy.

Add the eggs one at a time, beating well after each addition, then mix in the vanilla. Add the dry ingredients in three additions, alternating with the milk in two additions, and mix only until combined.

Divide the batter between the prepared pans and smooth the tops. Bake for 25–30 minutes, until the centers spring back lightly and a toothpick comes out clean or with a few moist crumbs.

Cool the cakes in their pans for 10 minutes, then turn them out onto wire racks. Cool completely before beginning the frosting.

Melt the butter in a heavy saucepan over medium heat, then add the brown sugar, evaporated milk or cream, and salt. Bring the mixture to a steady boil, stirring frequently, and cook to approximately 234–238°F (112–114°C), the soft-ball stage.

Remove the caramel mixture from the heat and stir in the vanilla. Let it cool for about 15–20 minutes, until warm rather than hot.

Gradually beat in the sifted confectioners’ sugar until the icing is thick and spreadable. Use it immediately because cooked caramel icing firms quickly as it cools.

Place one cake layer on a serving plate and spread it with frosting. Add the second layer, then frost the top and sides, working quickly; if the icing becomes too stiff, beat in 1–2 teaspoons of warm milk or cream.