Pecan Spice Layer Cake with Cream Cheese Frosting

Put oven rack in middle position and preheat oven to 350 °F. Butter and flour cake pans, knocking out excess flour. Sift together cake flour, baking powder, baking soda, salt, and spices into a large bowl. Beat together butter (1 1/2 sticks) and brown sugar in another bowl with an electric mixer (fitted with paddle attachment if using a stand mixer) at medium-high speed until pale and fluffy, 3 to 5 minutes. Beat in eggs 1 at a time, beating well after each addition, then beat in vanilla. Reduce speed to low, then add flour mixture and sour cream alternately in batches, beginning and ending with flour mixture and mixing until batter is just smooth. Mix in pecans until just combined. Spoon batter evenly into pans, smoothing tops, then rap pans once or twice to expel any air bubbles. Bake until pale golden and a wooden pick inserted in center of cakes comes out clean, 30 to 35 minutes. Cool 10 minutes in pans on racks. Run a thin knife around edge of pans, then invert racks over pans and reinvert cakes onto racks to cool completely.