Preheat oven to 350 degrees. Butter two 8-by-2-inch round cake pans; line with parchment rounds, and butter parchment. Dust with flour, tapping out excess. Sift together flour, baking powder, baking soda, and salt into a medium bowl.
With an electric mixer on medium speed, beat butter until softened, 1 to 2 minutes. Gradually add granulated sugar, and beat until pale and fluffy, 3 to 4 minutes, scraping down sides of bowl once or twice. Gradually add eggs; beat until incorporated after each addition, scraping down sides of bowl once or twice.
Slowly add the flour mixture in 3 batches, alternating with 2 batches of buttermilk; beat until just combined. Beat in vanilla and lemon zest.
Divide batter evenly between prepared pans. Bake, rotating halfway through, until a cake tester comes out clean, 35 to 45 minutes. Transfer pans to wire racks to cool 15 minutes. Turn out cakes onto racks to cool completely.
With a serrated knife, split each cake in half horizontally. Reserve the prettiest domed top for the top of the cake. Place the other top, dome-side down, on a cake stand or platter, and spread evenly with 1 cup lemon curd to within 1/2 inch of the edge. Top with second layer, and spread with another 1 cup curd. Repeat with third layer and remaining curd. Refrigerate cake to firm up lemon curd (or, if the kitchen is warm and the curd is too soft during assembly, refrigerate the layers as they are completed).
Just before serving, place the reserved domed layer on top of cake. Spoon whipped cream over top, and sprinkle with berries; dust with confectioners' sugar.