Butter and flour two 9-inch cake pans.
Sift together flour, baking soda, baking powder, and salt in a separate small bowl.
Stir together vanilla and sour cream in a small bowl.
Using a stand mixer with the paddle attachment, beat the butter and sugar until light and smooth.
Slowly add each egg, then one-third of the flour mixture, half the sour cream mixture, half the remaining flour mixture, the remaining sour cream mixture, and finally the remaining flour mixture.
Divide the batter among the prepared pans and bake for about 30 to 40 minutes or until a toothpick inserted into the center of the cake comes out clean.
Let the cakes cool completely before turning them upside down over a cake stand.
To make the frosting, melt the butter in a saucepan over medium heat, then stir in the brown sugar and cream.
Pour the mixture into a mixing bowl and beat at medium speed.
Slowly add the confectioners' sugar and vanilla until the frosting reaches the right consistency.
Spread about ¾ cup of frosting onto one cake layer and stack the other cake on top.
Frost the top and sides of the cake with a knife or spatula.