For the pudding: In a bowl, toss the blackberries with 1/2 cup of the granulated sugar. Set aside for 1 hour. Preheat the oven to 350°F. Spray a 9-by-9-inch baking dish with cooking spray. In a stand mixer with the paddle attachment, cream together the remaining 1 cup sugar and the butter. Add the eggs, one at a time, then the sour cream. Sift together the flour, cinnamon, and baking soda. Still beating, gradually mix that into the butter mixture until well incorporated. Fold the berries and their juice into the batter and pour the batter into the baking dish. Bake for 30 to 35 minutes. Meanwhile make the sauce: In a medium saucepan over medium-high heat, combine the brown sugar and butter and cook until the sugar melts, then until it starts to caramelize, about 8 minutes total. Off the heat, add the bourbon and cream. Return to the heat and whisk until smooth. Serve the pudding warm with the sauce on top.