Preheat oven to 425°F (218°C). Prepare a standard 12-cup muffin pan.
Make the streusel by combining the sugars and cinnamon, then mixing in melted butter and flour until large crumbs form.
Whisk the dry muffin ingredients. Separately, cream the butter and sugars for about 3 minutes. Add eggs, yogurt or sour cream, and vanilla.
Mix in the dry ingredients and milk until just combined. Fold in the chopped apples.
Fill muffin cups to the top, add streusel, and bake at 425°F for 5 minutes. Reduce to 350°F (177°C) and bake 15–18 minutes more.
Cool in the pan for 5 minutes, then transfer to a rack. Add optional icing after whisking it smooth.