Cake:
1 stick unsalted butter, softened, cut into ½-inch cubes
1¼ cups sugar
½ cup firmly packed light brown sugar
3 large eggs
2 cups all-purpose flour, sifted
1 cup well-shaken buttermilk
1 tsp baking soda
1 tbsp white vinegar
Frosting:
½ cup firmly packed dark brown sugar
1¼ sticks unsalted butter, at room temperature, cut into ½-inch cubes, divided
⅓ cup heavy cream
8 oz cream cheese, softened
¼ tsp salt
2 cups confectioners’ sugar, sifted
Topping:
Caramel sauce (e.g., Smucker's)
Preheat the oven to 350°F. Grease two 8" round cake pans, line them with parchment paper, and grease the parchment. Dust the parchment with flour and knock out the excess.
Beat the butter on medium speed until creamy, about 1 minute. Add both sugars and beat until fluffy, about 3 minutes. Add the eggs, one at a time, beating well after each addition. Add the flour in three parts, alternating with the buttermilk, beginning and ending with the flour. In a small bowl or cup, dissolve the baking soda in the vinegar and beat it into the batter until combined.
Divide the batter between the prepared pans and smooth the tops. Bake for 32 to 37 minutes, rotating the pans halfway through the baking time, until the cake tops are slightly browned and a toothpick inserted into the center of the cake comes out clean. Transfer the pans to a wire rack and let cool for 20 minutes. Turn the cakes out onto the racks and let cool completely. Remove parchment.
In a saucepan over medium heat, stir together the brown sugar and ½ stick of the butter until melted and combined. Bring the mixture to a boil and boil for 10-15 seconds. Remove from the heat, whisk in the cream, and transfer the mixture to a bowl to cool completely.
Once the brown sugar mixture is nearly cool, place the remaining 3 ounces of butter in a bowl and beat until it is lump free. Add the cream cheese and salt and continue beating until mixture is smooth. Turn the mixer to low and stream in the brown sugar mixture. Add the confectioners’ sugar, and beat until smooth. If the mixture feels too loose, refrigerate it for 5 to 10 minutes until it firms up.
Place one cake layer on a serving platter. Trim the top to create a flat surface and evenly spread about ¾ cup frosting on top. Place the next layer on top, then trim and frost it the same way. Frost the sides of the cake with the remaining frosting, drizzle with the caramel sauce and refrigerate the cake for 15 minutes to set before serving. Serve at just below room temperature.