Preheat oven to 350ºF. Prepare a 9-inch springform pan with nonstick cooking spray or butter. (Wrap bottom with foil to catchy any leaks, and/or bake on a baking sheet.)
In a large bowl, combine flour, flax seed, salt, baking powder, and baking soda. Set aside. In another large bowl, blend butter and preserves with electric mixer until light and fluffy. Add egg and vanilla and mix until well-combined. Next, add flour mixture alternately with buttermilk in two or three additions – mixing until just combined. Pour the batter into the prepared springform pan. Rinse the blackberries and scatter over the top of the batter. Sprinkle turbinado sugar over the top.
Bake for 40-45 minutes in a 350˚F oven or until cake tester inserted into middle of cake comes out clean. Cool on wire rack for 10 minutes, run a knife around edges, then release sides of pan. Continue cooling the cake until it is ready to be served — warm or at room temperature.
This cake is best eaten the day it’s made.
To make yogurt sauce, stir together 1 cup whole milk plain yogurt, 1/2 tsp. vanilla extract and 1/2 tsp. ground cinnamon.