Preheat oven to 325°F (160°C). Liberally grease a 10″ round pan with vegetable shortening. Cut out a 10-inch round of parchment paper, using bottom of pan as a template. Place inside pan, smoothing it out to cling securely to the shortening.
Puree black raspberries. Pour into small saucepan, straining out seeds if so desired. Add butter, flour, and brown sugar. Heat on low, stirring until well combined. Pour into prepared cake pan, spreading evenly. Drain pineapple slices, reserving the juice. Arrange pineapple slices on top of the black raspberry sauce, set aside.
Combine flour, sugar, baking powder, salt, and pudding mix in a large mixing bowl. Add in eggs and vodka, beating until smooth. Measure ⅔ cup of the reserved pineapple juice, add juice and melted butter to the mix, mixing on medium speed until smooth.
Carefully pour batter into prepared pan. Bake until golden and knife inserted into center of batter comes out clean and cake springs back – about 50-60 minutes.
While cake is baking, combine butter, water, sugar, and Chambord in a small saucepan. Allow to heat to a simmer, then remove from heat and allow to cool.
With the hot cake still in the pan, carefully level the top by cutting off the “dome” over the edge of the pan.
Evenly pour the Chambord syrup over the entire cake. Allow cake to cool for about 20 minutes before turning cake out directly onto serving plate. This cake is delicate, and should not be moved to a different plate after being turned out!