Make cake: Preheat oven to 350 degrees. Butter and flour a 9-inch round cake pan (2 inches deep). In a medium bowl, whisk together flour, baking powder, and salt. In a large bowl, using an electric mixer, beat eggs and sugar on high until pale and fluffy, 5 minutes. In a small saucepan, bring milk and butter to a simmer over medium. With mixer on medium, gradually add flour mixture to egg mixture and beat just until combined. With mixer on low, add milk mixture in a steady stream and beat until combined. Fold in vanilla.
Pour batter into pan. Bake until top is light golden and a toothpick inserted in center of cake comes out clean, 35 to 40 minutes. Let cool in pan on a wire rack, 10 minutes. Run a knife around edge of pan; turn cake out onto rack to cool completely (top side up), 30 minutes.
With a serrated knife, trim top of cake to make it level, then split cake in half horizontally. Place bottom layer on a cake plate or serving platter and spread jam evenly on top with an offset spatula. Top with second layer.
Make glaze: Place chocolate and corn syrup in a heatproof medium bowl. In a small saucepan, bring cream to a boil. Immediately pour over chocolate and let sit 2 minutes. Stir until mixture is smooth. Pour glaze on cake and spread with offset spatula so it drips down sides. Refrigerate until glaze is set, 45 minutes (or up to 2 hours). To serve, arrange cream puffs (if using) on top of cake.
If you like, make the cake layers up to a week in advance, then wrap tightly in plastic and freeze; thaw, loosely covered in plastic, at room temperature overnight.