Preheat oven to 350 degrees. Line muffin tin with papers.
Add butter and sugar to a large mixing bowl and beat until light and fluffy.
Beat in the egg and vanilla.
Stir in the applesauce.
Beat in the flour and baking soda until just combined. Do not overmix the batter.
Spoon mixture into the prepared muffin tin, filling 2/3 of the way full.
To make the streusel:
To prepare the streusel, add the sugar, flour, and cinnamon to a medium bowl and stir with a fork to combine.
Add the butter and use a fork or pastry cutter to cut the butter into the flour until the mixture is made of coarse crumbs.
Sprinkle the mixture evenly over all of the muffins.
Bake for 22 minutes or until a tester comes out clean. Cool completely.
To glaze:
When muffins are cool, whisk together the powdered sugar and milk and drizzle over the tops.
Video
Notes
Applesauce: You can use reglar applesauce here, but we like the punch of flavor that the cinnamon adds. Just stir in a teaspoon of cinnamon to the batter if you use plain applesauce. Glaze: The glaze is completely optional. You can skip it entirely for a less sweet muffin.