Combine the dry ingredients: In a medium bowl, whisk together the quick oats, flour, pumpkin pie spice, cinnamon, baking soda, baking powder, and salt. Set aside.
1½ cups quick-cooking oats, 2 cups all-purpose flour, 1½ tsp. pumpkin pie spice, 1/2 tsp. ground cinnamon, 1/2 tsp. baking soda, 1/2 tsp. baking powder, 1/2 tsp. kosher salt
Mix the wet ingredients: In a large mixing bowl, whisk together the slightly cooled melted butter, brown sugar, and granulated sugar until smooth and well combined. Add the pumpkin butter, egg, and vanilla and whisk again until fully incorporated.
1 cup unsalted butter, 1 cup light brown sugar, 1/3 cup granulated sugar, 1/3 cup pumpkin butter, 1 large egg, 1 Tbsp. vanilla extract
Make the cookie dough: Add the dry ingredients to the wet ingredients and fold together with a rubber spatula just until combined. Avoid overmixing.
Chill: Cover the cookie dough and refrigerate for 20-30 minutes Start Timer. Meanwhile, preheat the oven to 350°F and line a few baking sheets with parchment paper or silicone baking mats.
Scoop and shape: Scoop the dough into approximately 2 Tbsp. portions and arrange on the prepared baking sheets, leaving about 2 inches between each cookie. Gently flatten the tops of the dough balls with your fingers. This helps the cookies spread into that classic iced oatmeal cookie shape.
Bake: Bake for 10-12 minutes (always underbake) Start Timer, or until the edges are set but the centers still look slightly soft. Avoid overbaking. If needed, after removing the cookies from the oven, use a large round cookie cutter or glass to gently "scoot" each cookie into a perfectly round shape if any lost their perfect circular cookie shapes. Allow the cookies to cool on the baking sheet for about 5 minutes before transferring to a wire rack to cool completely. Start Timer
Make the glaze: In a small bowl, whisk together the powdered sugar, 2 tablespoons milk, corn syrup, vanilla, and a pinch of salt until smooth. Add additional milk, a little at a time, until you have a thick but dip-able glaze.
1½ cups powdered sugar, 2-3 Tbsp. whole milk, 1 Tbsp. light corn syrup, 1/2 tsp. vanilla extract, Pinch of salt
Ice the cookies: Once the cookies are completely cool, lightly dip the tops into the glaze, allowing some of the cookie's textured surface to peek through for that classic iced oatmeal cookie look. Place back on the wire rack and allow the glaze to set before serving.