Make the burnt sugar by placing 1/2 cup of white sugar into a heavy skillet over medium-high heat. Stir constantly with a wooden spoon as the sugar melts. When the sugar turns very dark brown, remove the skillet from heat. Slowly add the hot water while stirring until the sugar dissolves. Set this mixture aside to cool.

Preheat the oven to 350 degrees F (175 degrees C). Line two 9-inch round baking pans with parchment paper.

Sift together the cake flour, baking powder, and salt three times.

Cream the butter with the remaining 1 1/4 cups of white sugar until the mixture is light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract and the cooled burnt sugar syrup.

Alternately add the sifted dry ingredients and the milk to the creamed mixture, beating until the batter is smooth. Pour the batter evenly into the prepared pans.

Bake the cakes at 350 degrees F (175 degrees C) for 25 to 30 minutes.