Heat oven to 350 degrees. Arrange two racks in center of oven. Butter two 8-by-2-inch round cake pans; line bottoms with parchment paper. Dust bottoms and sides of pans with flour; tap out any excess.
In a large bowl, sift together flour, baking powder, baking soda, and salt.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter on medium speed until softened, 1 to 2 minutes. Gradually add granulated sugar, beating on medium speed until lightened, 3 to 4 minutes; scrape down sides once or twice. Drizzle in eggs, a little at a time, beating after each addition until batter is no longer slick, about 5 minutes; stop once or twice to scrape down sides.
On low speed, alternately add flour mixture and buttermilk, a little of each at a time, beginning and ending with flour mixture. Beat in vanilla and lemon zest.
Divide batter evenly between the prepared pans. Bake 25 minutes, then rotate the pans in the oven for even browning. Continue baking until a cake tester inserted into the center of each cake comes out clean, 10 to 20 minutes more. Transfer pans to wire racks to cool, 15 minutes. Turn out cakes; set on racks, tops up, until completely cool.
Remove the parchment from bottom of each cake. Using a serrated knife, slice each layer in half horizontally. Set aside the prettiest domed layer for the top of cake. Place another domed layer, dome-side down, on a serving platter. Spread 1 cup lemon curd over surface to within 1/2 inch from edges. Place second cake layer over the first, and spread another 1 cup curd over top. Repeat with third cake layer and remaining cup curd. Transfer partially assembled cake to the refrigerator.
Just before serving, place reserved dome on top of cake. Spoon sweetened whipped cream over the top. Sprinkle with mixed berries, and dust with confectioners' sugar through a fine sieve.