Make the cake: Preheat oven to 350°F. Line bottom of a buttered 9-by-2- inch round cake pan with a round of wax paper, then butter the paper. Sift together flour, baking powder, baking soda and salt. Beat together butter and sugar in a large bowl with an electric mixer until pale and fluffy, then beat in vanilla. Add eggs one at a time, beating well after each addition, then, with mixer at low speed, beat in all of buttermilk until just combined. Add flour mixture in 3 batches, mixing after each addition until just combined.
Spoon batter into cake pan, smoothing top, and bake in middle of oven until golden and a tester comes out clean: usually 40 to 50 minutes. Cool in pan on a rack for 10 minutes, then run a thin sharp knife around edge of cake to loosen from pan. Invert onto rack, then slide cake onto a cake plate.
Make the topping: Bring wine, 3 tablespoons sugar, and zest to a boil in a small heavy saucepan, stirring until sugar is dissolved. Boil until syrup is reduced to about 2/3 cup: usually 1 to 2 minutes. Discard zest. Reserve 2 tablespoons syrup and pour remainder slowly and evenly over cake (cake will absorb syrup). Stir together the reserved syrup, preserves, and remaining tablespoon sugar in small saucepan and simmer, stirring occasionally, until thickened slightly: usually about 1 minute (it should be the consistency of a thick syrup). Put blackberries in a large bowl, then pour preserves mixture over berries. Gently stir berries with a rubber spatula to coat, then pour over cake, mounding blackberries on top. Serve warm or at room temperature.
Cake (without syrup and topping) can be made one day ahead, cooled completely, then kept at room temperature, wrapped in plastic wrap.
Yield: 8 servings.