Brown the butter: Melt 1 cup butter in a skillet over medium heat, stir constantly until deep brown and toasty, then pour into a bowl to cool completely.
Preheat oven: Heat oven to 350°F and line baking sheets with parchment paper so cookies won't stick.
Blot pumpkin: Spread ⅔ cup pumpkin on a plate, press paper towels firmly into it until the moisture absorbs and the pumpkin sticks.
Mix wet ingredients: Add cooled butter, 1 cup brown sugar, ½ cup granulated sugar, blotted pumpkin, 2 egg yolks, and 2 teaspoons vanilla, stir well.
Combine dry ingredients: Whisk 2⅓ cups flour, 2 teaspoons pumpkin spice, 1 teaspoon baking soda, ½ teaspoon baking powder, and 1 teaspoon salt together.
Make dough: Gradually add dry ingredients to wet mixture, stir until no flour streaks remain without overmixing the dough.
Add oats: Fold 2 cups oats into the dough until evenly mixed throughout for a hearty texture in every bite.
Shape cookies: Scoop 3 tablespoons (66g) of dough, roll into balls, space 2 inches apart on baking sheets.
Bake: Place on center rack, bake 12 minutes until edges set but centers look slightly underdone.
Cool: Let cookies rest on the sheet 5-10 minutes, transfer to a cooling rack, and cool completely before glazing.
Make glaze: Whisk 1¼ cups powdered sugar, 1 tablespoon brown sugar, 1½ tablespoons milk, 1 tablespoon corn syrup, and ¼ teaspoon vanilla smooth.
Drizzle and serve: Use a whisk to drizzle glaze over cooled cookies, let set 15-20 minutes before enjoying.