For the cake: preheat the oven to 350° F. Butter and flour two 6-inch by 3-inch tall round cake pans. Invert the pans and tap them firmly on the sides to shake out the excess flour.
Sift together the flour, baking powder, and salt. In a separate large bowl, beat the butter on medium speed until smooth and creamy. Add the sugar and continue beating until the mixture is light yellow and fluffy, 2-3 minutes. Beat in the eggs, one at a time. Add the vanilla.
Turn the mixer on low and gradually add the dry ingredients until just blended.
Spoon equal amounts of batter into each pan and smooth the tops evenly. Bake for about 30-40 minutes, or until light golden and a cake tester comes out clean. Let the layers cool in the pans for 10 minutes, then unmold onto wire racks to cool completely.
Using a long, sharp knife, cut the tops of the cake so that the tops are even. Cut the cake again horizontally in half so that you end up with four layers. Wrap in plastic wrap until you are ready to ice them to prevent the cakes from drying out.
To ice the cakes, pipe icing around the outer edges of the first layer, then fill in the center with more icing. Using a spatula, gently smooth out the layer of icing. Gently place the second layer on top of the first, pushing down gently so that some of the icing oozes out. Repeat with each layer. Run an icing spatula along the sides of the cake where the icing has oozed out to create uneven "streaks" of icing on the sides.
Arrange peach slices on top of cake in a circular pattern. Garnish with rosemary. Serve immediately.