Preheat oven to 375°F (190°C) and line a 12-cup muffin tin with paper liners.
Prepare the streusel by combining melted butter, brown sugar, flour, and a pinch of salt in a bowl; mix with a fork until crumbly and set aside.
Make the cheesecake filling by beating softened cream cheese, egg yolk, and sugar until smooth and creamy; set aside.
In a mixing bowl, cream together softened butter, granulated sugar, and brown sugar until light and fluffy.
Add eggs one at a time, mixing well after each addition, then blend in yogurt and vanilla extract.
In a separate bowl, whisk together all-purpose flour, baking soda, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture and mix until just combined.
Gently fold in the frozen mixed berries, being careful not to thaw.
Fill each muffin cup halfway with batter, spoon about 1 tablespoon of cheesecake filling into the center, then cover with remaining batter.
Generously sprinkle the streusel topping over each muffin.
Bake for 18 to 22 minutes until muffins are golden and a toothpick inserted into the muffin (avoiding cheesecake center) comes out clean.
Allow muffins to cool in the pan for 10 minutes before transferring them to a wire rack to cool completely.