Preheat oven to 375°F (190°C). Line a muffin tin with paper liners or grease lightly.
In a bowl, beat cream cheese, sugar, and vanilla extract until smooth. Set aside.
In a large bowl, whisk together flour, sugar, baking powder, and salt.
In another bowl, whisk egg, milk, oil, and vanilla extract until smooth.
Pour wet ingredients into dry ingredients and mix gently until just combined.
Fold blueberries carefully into the batter.
Fill muffin cups halfway with batter.
Add a spoonful of cream cheese filling to the center of each muffin.
Top with additional batter until cups are about ¾ full.
Add coarse sugar or crumb topping if desired.
Bake for 18–22 minutes until tops are golden brown and a toothpick inserted near the edge comes out clean.
Cool slightly before serving.