Preheat your oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper or lightly grease it.
In a large bowl, beat together the sugar and softened butter until light and fluffy.
Add the eggs, sour cream, and vanilla extract. Mix until well combined.
Whisk together the flour, salt, and baking powder in a separate bowl. Gradually add to the wet mixture and stir until just combined.
Spread the batter evenly in the prepared baking pan.
For the cream layer: In another bowl, beat the softened cream cheese, sugar, egg, and vanilla until smooth and creamy. Gently spread this mixture over the batter in the pan.
Scatter the fresh mixed berries evenly over the cream layer.
Bake for 28-32 minutes or until the center is set and the edges are golden.
Let cool completely in the pan before slicing into bars. Dust with powdered sugar before serving, if desired.