In a large mixing bowl, beat melted butter with granulated sugar and brown sugar until creamy. Add pumpkin puree and mix until fully combined. Stir in cinnamon, nutmeg, kosher salt, baking soda, baking powder, oats, and flour until just blended.
Fold in white chocolate morsels gently until evenly distributed.
Drop cookie dough by large tablespoonfuls onto a parchment-lined baking sheet. Bake in a preheated oven at 350°F for 14 to 16 minutes. Remove and let cool completely before glazing.
For the glaze, whisk powdered sugar, maple flavoring, and milk together until smooth. Drizzle or spoon glaze over cooled cookies. Allow glaze to set for about 15 minutes before serving.
Notes
These pumpkin oatmeal cookies keep well in an airtight container for up to 5 days. The maple glaze can be omitted or substituted with a simple powdered sugar glaze if desired.