Preheat oven to 350 degrees. Spray an 8x8 inch pan with cooking spray and set aside.
In a medium sized bowl, whisk together the all-purpose and whole-wheat flours, the baking soda and salt. In a small bowl, stir together the granulated sugar, cinnamon and walnuts. In a large bowl, beat the brown sugar, butter and oil until fluffy. Beat in the eggs one at a time until incorporated, and lastly add the vanilla and yogurt.
Spread half of the batter into the 8 inch pan. Sprinkle half of the nut mixture over the batter and top with the blueberries. Gently pressing them into the batter. Spoon the rest of the batter over the top and smooth it out. Sprinkle the remaining mixture over the top of the cake.
Bake 30-35 minutes or until a toothpick inserted comes out clean. Let cool slightly and then unfold and allow to cool completely. Cut into two inch squares.