Preheat oven to 350 degrees. Flour and grease three 14” round cake pans, three 10” pans, and three 6” pans. In a mixer, cream butter and sugar until fluffy and light in color. Beat in eggs on low; mix until smooth. Beat in vanilla. Transfer the mixture to a large bowl.
In a separate bowl, sift flour, baking powder, and salt. Stir one-third of the flour mixture into the butter and eggs until just smooth. Stir in half of the milk. Continue alternating between mixing flour mixture and the milk into the butter-egg mixture. Do not overmix. Divide batter into the nine baking pans. Layers should be about 1” deep.
Bake until cakes are golden, springy to the touch, and just pulling away from the sides of the pans. Ovens may vary, so to avoid over-baking, check after 20 minutes and every 3 to 5 minutes thereafter.
Remove cakes from pans and place on cooling racks. While cooling, construct three cardboard rounds (14”, 10”, and 6”) that will support the three tiers of the cake.
Assemble with peach syrup and peach mousse filling. Frost with buttercream icing. Keep cool, enjoy.