1. Make the cake: Preheat oven to 350 degrees, with rack in center position. Butter two 9-inch round cake pans (2 inches deep); line with parchment cut to fit. Butter parchment; dust with flour, tapping out excess. Whisk together flour, baking powder, baking soda, and 1 teaspoon salt.

2. Beat butter and granulated sugar with a mixer on medium-high speed until pale and fluffy, scraping down sides of bowl as needed, about 2 minutes. Reduce speed to medium, and add eggs, 1 at a time, beating well after each addition. Beat in flour mixture, alternating with buttermilk, beginning and ending with flour. Beat in vanilla.

3. Divide batter between pans. Bake, rotating halfway through, until tops spring back when gently touched and a cake tester inserted into centers comes out clean, about 40 minutes. Transfer to wire racks, and let cool in pans for 20 minutes.

4. Run a knife around edge of cakes, and invert onto racks; remove parchment, and let cool completely.

5. Make the filling: Combine strawberries with granulated sugar, lemon juice, and 1/4 teaspoon salt. Let stand, stirring occasionally, for 30 minutes. Strain, reserving syrup.

6. Whisk cream with confectioners' sugar until medium peaks form.

7. Trim cake tops. Slice cakes in half horizontally. Generously brush 1 cake layer with some reserved syrup, and spread on one-third of the jam. Top with one-third of the filling, then one-third of the whipped cream. Repeat with 2 more cake layers. Top with remaining cake layer, bottom side up. Refrigerate for at least 1 hour or up to 2 hours. Dust cake with confectioners' sugar just before serving.