Preheat the oven to 400 degrees F. Grease a 9-inch cake pan with non-stick cooking spray.

In a medium bowl, combine the flour, baking powder and salt.

In a large bowl, rub 1 cup sugar with the lemon zest until the sugar is moist like wet sand. Whisk in the yogurt, vegetable oil, eggs and vanilla extract. Fold in the dry ingredients until just combined.

In a small bowl, use a fork to mash the berries with 1 tablespoon granulated sugar.

Spread 1 cup batter into the bottom of the prepared baking pan and spoon over half the blackberries. Spread on the remaining batter into an even layer and top with the rest of the blackberries.

Bake for 30-35 minutes until the top of the cake is golden brown and a toothpick inserted in the center comes out clean.

Cool the cake in the pan for 15 minutes before removing and cooling on a wire rack. Serve warm or at room temperature.