Preheat the oven to 350°F (175°C) and grease a 9x5-inch loaf pan.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
In a large bowl, beat butter and sugar until light and fluffy. Add eggs, one at a time, and mix well. Stir in vanilla extract.
Mix in the sour cream and milk, alternating with the flour mixture, until just combined.
Gently fold in blueberries.
In a separate bowl, beat cream cheese, sugar, egg yolk, and vanilla extract until smooth.
Pour half the batter into the prepared pan. Spread the cream cheese mixture over the batter, then top with the remaining batter.
Bake for 50-60 minutes or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.