Preheat oven to 350°F. Grease and line a 9-inch cake pan with parchment.
Mix dry ingredients: In a bowl, whisk flour, baking powder, and salt.
Mix wet ingredients: In another bowl, whisk sugar, yogurt, oil, eggs, and vanilla until smooth.
Combine: Slowly whisk dry into wet ingredients until smooth and mostly lump-free.
Bake: Pour into prepared pan. Bake 35–40 minutes or until toothpick comes out clean.
Cool: Let cool in the pan for 10 minutes, then invert and cool completely.
Make frosting: Beat cream cheese until smooth. Add yogurt, powdered sugar, and vanilla. Whip until fluffy.
Frost: Spread over cooled cake. Garnish with berries if desired.