In a large bowl, stir together the coconut sugar, pumpkin puree, melted butter and applesauce until smooth. Add the egg and vanilla and stir until well-combined.
Stir in the oats, baking soda, pumpkin pie spice, and salt. Add the whole wheat pastry flour and stir until just combined.
Cover the bowl with plastic wrap and refrigerate for 1 hour. In the meantime, preheat the oven to 350° and line a large baking sheet with parchment paper.
After an hour, scoop the cookie dough into 12 balls (roughly ¼ cup dough each). Flatten each cookie dough ball slightly with your hand, then bake in the preheated oven for 14-16 minutes.
Allow the cookies to cool completely, then make the glaze by whisking together the powdered sugar and 1 tbsp milk. If too thick, add ½ tbsp of milk at a time until it reaches a consistency that you can drizzle. *See notes*
Drizzle or spoon the glaze onto the cooled cookies, allowing the glaze to drip off the cookies. Allow the glaze to set for at least 1 hour before serving.
Notes
Note on the glaze: the glaze does not stay set for more than 1 day. I would recommend glazing the day you'd like to serve them for best results.