Preheat oven to 425°F and prepare a muffin pan with paper liners.
Prepare the crumb topping by mixing flour, brown sugar, salt, and melted butter until coarse lumps form; set aside.
In a small bowl, whisk the cream cheese, granulated sugar, corn starch, and vanilla until smooth and creamy for the filling.
In a large bowl, whisk together flour, baking powder, and salt.
In a separate medium bowl, combine egg, sugar, oil, vanilla, and Greek yogurt until pale and uniform.
Fold the wet mixture into the dry ingredients using a spatula until just combined.
Gently fold in half of the berries.
Fill muffin cups halfway with batter, add a spoonful of the cream cheese mixture, then top with remaining batter and berries.
Sprinkle with the crumb topping.
Bake at 425°F for 5 minutes, then reduce heat to 375°F and bake for an additional 30 minutes until golden brown.