Preheat oven to 425°F (218°C). Spray a 12-count muffin pan with nonstick spray or line with cupcake liners.

Make the crumb topping: Mix the brown sugar, granulated sugar, and cinnamon together in a medium bowl. Stir in the melted butter, and then gently mix in the flour using a fork.

Make the muffins: Whisk the flour, baking soda, baking powder, cinnamon, and salt together in a large bowl.

Using a handheld or stand mixer, beat the butter and both sugars together on high speed until smooth and creamy, about 3 minutes. Add the eggs, yogurt, and vanilla extract. Beat until mostly creamy.

With the mixer running on low speed, add the dry ingredients and milk into the wet ingredients and beat until no flour pockets remain. Fold in the apples.

Spoon the batter evenly into each cup, filling each all the way to the top. Spoon crumb topping on each, gently pressing it down.

Bake for 5 minutes at 425°F, then reduce to 350°F (177°C) and bake for an additional 15-18 minutes.

Allow the muffins to cool for 5 minutes in the muffin pan, then transfer to a wire rack.

Make the icing: Whisk all of the icing ingredients together and drizzle over warm or cooled muffins.

Iced or plain muffins stay fresh covered at room temperature for a few days or in the refrigerator for up to 1 week.