Preheat an oven to 350F and place 9 silicone baking cups on a baking sheet or spray a muffin tin with nonstick cooking spray. Set aside.
Mix the dry ingredients for the muffins together in a large bowl. In a separate bowl, whisk together the egg, milk, and apple sauce together before adding to the dry ingredients. Stir the muffin batter until smooth.
Fill each baking cup 3/4 full with the muffin batter. Set aside.
Add the butter, walnuts, oats, and Swerve brown to another bowl and stir together before adding to the top of each baking cup.
Bake for 25-30 minutes until a toothpick or knife comes out clean. Transfer the muffins to a wire rack to cool.
For the glaze, mix the Swerve confectioners and water together and drizzle over the top of the cooled muffins.