Preheat your oven to 425°F (218°C). This high temperature helps create tall, bakery-style muffin tops. Line a 12-cup muffin pan with paper liners and lightly grease any extra cups if you are using them.
In a bowl, combine brown sugar, granulated sugar, cinnamon, melted butter, and flour for the crumb topping. Mix everything together with a fork until the mixture forms clumps and looks crumbly. Once done, place it in the refrigerator so it stays firm and crunchy while you prepare the batter.
In a large bowl, whisk together flour, baking soda, baking powder, cinnamon, and salt until evenly combined. This ensures the muffins rise properly and the spices are evenly distributed throughout the batter.
In another mixing bowl, beat the softened butter with brown sugar and granulated sugar for about 2–3 minutes until the mixture becomes light, fluffy, and pale in color. This step helps create a soft and airy muffin texture.
Add the eggs one at a time, mixing well after each addition. Then add yogurt (or sour cream) and vanilla extract, and mix until smooth. It is normal if the mixture looks slightly curdled at this stage, as it will come together once the dry ingredients are added.
Gradually add the dry ingredients into the wet mixture, alternating with milk. Mix gently using a spatula or on low speed, just until everything is combined. Avoid overmixing, as this can make the muffins dense instead of soft and fluffy.
Gently fold in the chopped apples using a spatula, making sure they are evenly spread throughout the batter so every muffin has good apple pieces. Be careful not to overmix at this stage.
Spoon the batter into the prepared muffin cups, filling each about three-quarters full. Take the chilled crumb topping and generously sprinkle or press it on top of each muffin to create a thick, bakery-style layer.
Bake the muffins at 425°F (218°C) for 5 minutes, then without opening the oven door, reduce the temperature to 350°F (177°C) and continue baking for 16–17 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
Let the muffins cool in the pan for about 5 minutes before transferring them to a wire rack to cool completely. If you want to add glaze, mix powdered sugar, cream (or milk), and vanilla until smooth, then drizzle it over the slightly warm muffins for a bakery-style finish.