Many Southern cooks use an often-tricky caramel-fudge recipe to frost their cakes; this one opts for caramel syrup throughout, for flavor and moisture, and a dependable brown-butter frosting.
To make the caramel syrup: In a small, heavy saucepan, combine the sugar with 1/3 cup (74g) water. Cook over medium heat without stirring until the sugar melts, the water boils away, and the syrup and begins to turn color.
When the sugar is a medium amber color, remove the pan from the heat and slowly pour in 3/4 cup (170g) water. The mixture will bubble and spurt, so be careful. Once all of the water is in the pan, return the pan to low heat and stir until the sugar melts and you have a smooth liquid. Remove from the heat and cool to room temperature.
To make the cake: Preheat the oven to 350°F. Grease two 9" cake pans, and line them with parchment.
In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt. Add the butter and beat at low speed until the mixture looks sandy.
Combine the 1/2 cup (160g) caramel syrup, vanilla, and sour cream; add all at once to the flour mixture, and mix until fully incorporated. Scrape the sides and bottom of the mixing bowl, then beat in the eggs, one at a time. Scrape the bowl, beat for one minute more, and divide the batter between the prepared pans.
Bake the cakes for 25 to 27 minutes, until a light touch in the center springs back, and the cake just begins to pull from the sides of the pan. Remove them from the oven and cool them in their pans on a rack.
To make the frosting: Place the butter in a 2-quart, heavy-bottomed saucepan. Melt over medium-low heat. Cook until the butter foams and begins to spurt; eventually the solids will begin to caramelize and the butter will begin to smell nutty. Once this happens, remove it from the heat and pour it into a mixing bowl. Let the butter cool to room temperature.
Add the caramel syrup, vanilla, and salt. Add the confectioners' sugar and mix; the mixture will get stiff and lumpy (that's OK).
Add the heavy cream a tablespoon at a time while the mixer is running; the frosting will magically smooth out. When the frosting is a little stiffer than you want for a spreading consistency, scrape the sides and bottom of the mixing bowl, and add one more tablespoon of cream. The icing should become smooth and quite spreadable.
To assemble: Flip the cooled cake layers out of their pans; trim the tops to be level, if necessary. Place one layer, top down, on a serving plate. Line the plate with strips of parchment or waxed paper to keep it clean while you frost the cake.
Spread 2/3 cup of frosting over the first layer. Place the second layer, top side down, over the filling. Cover the top and sides of the cake with the remaining frosting.
To garnish: Take thickened caramel syrup (see baker's tips, above left), cooled to room temperature, and drizzle it over the top of the cake before cutting.
