Brown the butter: Melt the butter in a small pan over medium heat until it smells nutty and turns golden brown, then remove from heat and let it cool.
Prepare the crumble topping: In a small bowl, mix the flour, brown sugar, cinnamon, and melted butter with a fork until crumbly, then set aside.
Preheat the oven: Heat your oven to 350°F and line a muffin tin with paper liners or grease it well.
Mix dry ingredients: In a medium bowl, whisk together the flour, baking soda, baking powder, salt, and cinnamon.
Mix wet ingredients: In a large bowl, whisk the eggs, granulated sugar, brown sugar, yogurt, milk, vanilla, and cooled brown butter until smooth.
Combine wet and dry: Gently fold the dry ingredients into the wet ingredients just until combined.
Add the apples: Stir in the chopped apples until evenly distributed through the batter.
Fill the muffin cups: Divide the batter evenly between the 12 muffin cups, filling them about ¾ of the way.
Add crumble topping: Spoon the crumble topping evenly over each muffin and gently press it down so it sticks.
Bake: Bake for 18–20 minutes or until a toothpick inserted into the center of a muffin comes out clean.
Cool: Let the muffins cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.