For the cake: Preheat oven to 350-degrees and butter and flour an 8 by 2-inch round cake pan. In a large bowl with an electric mixer, beat together butter and sugar until light and fluffy. Add remaining cake ingredients and beat on low speed until pale yellow, about 3 minutes. Pour batter into prepared pan and bake in middle of oven for 40 minutes, or until a tester comes out with a few crumbs adhering.
For the Rosemary Syrup: In a small saucepan simmer all syrup ingredients except vanilla. Cool syrup 30 minutes and strain through a sieve into a 2-cup measure. Add vanilla.
Cool the cake in the pan on a rack 10 minutes. Invert cake onto hand and return, right side up, to a rack. While cake is still warm, gradually brush 1/3 cup syrup over it, allowing syrup to soak in before adding more. Chill remaining syrup in a small pitcher, covered. Syrup-soaked cake may be made 1 day ahead and kept wrapped in plastic wrap at room temperature.
Serve the cake, cut into wedges, with whipped cream, blackberries and remaining Rosemary Syrup.