Preheat oven to 350 degrees. In a bowl, whisk both flours with baking powder and salt; set aside.
In a mixing bowl, cream butter and sugars until light and fluffy. Add eggs and vanilla, one at a time, beating well. Set aside.
In separate bowl mix together milk and lemon juice; add in yogurt and stir to combine.
Next, combine all wet ingredients together. Turn mixer on low-speed and slowly add flour mixture to wet ingredients; mixing until just combined.
In a bowl, gently smash blackberries into smaller pieces and mix with the teaspoon of flour. Add your lemon zest and stir again.
Coat a 12-cup nonstick Bundt pan with cooking spray. Spread 1/4 of batter in prepared pan. Layer with blackberries. Spread another 1/4 of batter on top of blackberries. Continue to do this until all of the blackberries are gone.
Bake cake on bottom rack of oven until a toothpick inserted into center of cake comes out clean, 40-50 minutes.
Cool in pan 20 minutes. Invert onto a rack; cool completely, top side up.
Dust with confectioners' sugar before serving, if desired. Or make the lemon cream cheese glaze.
To make the lemon cream cheese glaze: Combine lemon zest, cream cheese, 1 tablespoon milk, and powdered sugar in medium bowl. Drizzle over cake.