Preheat Oven: Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
Mix Dry Ingredients: In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, nutmeg, and cloves. Set aside.
Cream Butter and Sugars: In a large bowl, beat softened butter, granulated sugar, and brown sugar until light and fluffy.
Add Wet Ingredients: Beat in egg and vanilla extract until combined. Mix in pumpkin puree until smooth.
Combine Dry and Wet Ingredients: Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Form Cookie Balls: Scoop 1–2 tbsp of dough and roll into balls. Place on prepared baking sheets 2 inches apart.
Bake the Cookies: Bake for 10–12 minutes, until edges are set but centers are soft.
Cool the Cookies: Let cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Prepare the Glaze: In a small bowl, beat cream cheese until smooth. Add powdered sugar, vanilla, and milk gradually until a pourable glaze forms.
Glaze the Cookies: Drizzle or spread cream cheese glaze over cooled cookies. Allow glaze to set for at least 15 minutes before serving.