Preheat the oven to 400°F and prepare a muffin tin by lightly greasing it or lining it with muffin liners.
In a medium bowl, combine the flour, brown sugar, and cinnamon for the crumble topping. Work in the cold butter using a fork or your hands until the mixture becomes crumbly, then set aside.
In another bowl, whisk together the flour, baking powder, baking soda, and salt for the muffin batter.
In a large bowl, whisk the yogurt, sugar, eggs, vegetable oil, milk, and vanilla extract until smooth and well combined.
Toss the blueberries with a small amount of flour in a separate bowl to help them stay evenly distributed in the batter.
Add the dry ingredients to the wet ingredients and gently stir until just combined. Fold in the blueberries carefully without overmixing.
Divide the batter evenly among the muffin cups, then sprinkle the crumble topping over each portion.
Bake until the tops are golden and spring back when touched, and a toothpick inserted in the center comes out clean.
Allow the muffins to cool in the pan briefly before transferring them to a wire rack to cool completely.