Preheat the oven to 350 degrees F. If using frozen berries, thaw at room temperature 15 minutes; drain.
For the filling, place yogurt in a large mixing bowl, sprinkle with the 2 tablespoons flour. Add 1/2 cup sugar, egg yolks, whole egg, lemon zest, salt, and 1 teaspoon vanilla. Mix until smooth; set aside.
In a medium mixing bowl, sift together 1 cup flour, 1/2 cup sugar, salt, and baking powder. Add butter, egg whites, and 1 teaspoon vanilla. Gently stir everything together by hand until mixed well. (Mixture will be like soft cookie dough.) Spread onto the bottom of an ungreased 9-inch springform pan; sprinkle berries on top. Pour the filling prepared earlier over the berries.
Bake the kuchen for about 55 minutes or until center appears set (slightly wobbly) when shaken gently. Cool in the pan on a wire rack for 15 minutes; undo the clasp on the side of the pan and remove the ring. Cover the kuchen and chill it in refrigerator for 4 to 24 hours.
To serve, remove the pan bottom. Transfer to a platter.