Prepare the cake pan. Preheat an oven to 375°F / 190°C, then line an 8-inch cake pan with parchment paper and coat with baking spray.
Make the blueberry purée. Place 8 oz blueberries and 3 Tbsp blueberry jam in a blender. In a small bowl, mix together 2 tsp cornstarch and 2 tsp pure vanilla extract to form a slurry. Add to the blender, then purée until smooth. Set aside.
Whisk dry ingredients, then add butter. In a large bowl, whisk together 120g all-purpose flour, 120g pastry flour, 150g sugar, ½ tsp Kosher salt, 1 tsp baking powder, and ½ tsp baking soda. Add 12 Tbsp cubed butter and break apart with your fingers or a pastry cutter until butter is the size of small peas. Remove and reserve ½ cup of flour mixture to crumble on top of cake.
Add the wet ingredients. In the same bowl as the flour mixture, add in 240g sour cream, 1 large egg, and 1 Tbsp vanilla extract. Mix using a spatula until very well mixed.
Assemble the cake. Pour slightly more than half of the cake batter into the prepared dish. Using slightly damp hands, gently push down the batter to form an even layer, pushing up slightly along the sides of the pan.
Add the blueberry purée. Pour the blueberry purée mixture evenly on top, leaving a roughly 1-inch border around the edge untouched. Carefully dollop the remaining cake batter on top. Dampen your hands again slightly, then gently spread out the batter as best you can.
Bake. Add 2 tsp cinnamon and 2 tsp turbinado sugar to the reserved ½ cup flour mixture, then sprinkle evenly on top. Bake until golden brown on the edges and a cake tester inserted into the center of the cake comes out clean, about 40 minutes. Cool completely before serving.