Preheat oven to 350°F and grease a loaf pan.
Whisk together flour, baking powder, baking soda, and salt in a bowl.
Cream butter and sugar until light and fluffy. Beat in eggs and vanilla.
Mix in sour cream, then fold in dry ingredients until just combined.
Gently fold in blueberries.
Spread half of batter into prepared pan.
Mix cream cheese with powdered sugar until smooth, then spread over batter.
Add remaining batter on top, smoothing gently.
Bake 55 to 65 minutes, or until a toothpick comes out clean.
Cool before slicing.