In the bowl of a stand mixer fitted with a paddle attachment (or using a hand mixer), cream butter. Add brown sugar and granulated sugar. Mix until smooth. Add egg, molasses, and apple sauce.
In a bowl, whisk together flour, cinnamon, baking soda, baking powder and sea salt. Add to mixing bowl. Fold in rolled oats and walnuts.
Use a 1 ½- inch scoop to portion out cookies. Arrange on parchment lined baking sheet at least 2 inches apart. Bake for 13-15 minutes, rotating pans midway through baking. Allow to cool in pan for 3 minutes before transferring to wire rack to cool to room temperature.
Maple Glaze: Whisk together powdered sugar, maple syrup, salt and milk until smooth. If glaze is too thick, add additional milk 1 tsp at a time until desired consistency is achieved. Drizzle glaze over cooled cookies. Enjoy immediately, or allow glaze to harden and set.