Preheat oven to 375°F and line muffin tin with 6 liners.
In a small saucepan, combine apples, butter, brown sugar, and cinnamon. Bring to a simmer, and cook until apples are softened and sugar is caramelized, 4 to 6 minutes. Remove from heat and set aside.
In a small bowl, whisk together flour, baking soda, cinnamon, all spice, and salt.
In a medium bowl, cream softened butter and sugar. Add egg white, yogurt/sour cream, and vanilla, and mix well. Stir in flour mixture until just combined. Fold apples into the mixture, making sure to scrape all the caramelized sugar out of the pan with them. Fold just until apples are distributed throughout the batter. You don't want to completely mix in the swirls of sugar and cinnamon.
Divide batter between prepared muffin cups.
In a small bowl, stir together flour, brown sugar, and cinnamon. Add in melted butter and stir until completely mixed. The mixture is going to seem a little wet, but don't worry about it. Drop small scoops of the streusel over the top of your muffins. Bake for 15 to 18 minutes, until a toothpick inserted into the center comes out clean.
Cool in the pan for 10 minutes before transferring to a cooling rack.
*1 cup diced apples is equal to about 1 large apple. If you are a little over or under 1 cup, don't worry about it. Granny Smith Apples are my preferred baking apples, but most apples (not Red Delicious) will work fine for these muffins.*If using salted butter, simply cut the salt to a pinch where salt is called for in the recipe.Muffins are best on the first day, but you can store them at room temperature in an airtight container for up to 3 days.