Preheat oven to 350 degrees. Line a baking sheet with parchment paper or silicone baking mat and set aside. In a large bowl, stir butter, oil, pumpkin, sugars, vanilla and eggs together until incorporated and smooth. Slowly mix in all dry ingredients until completely incorporated. Scoop onto prepared baking sheet using 1 1/2 tablespoon scoop and flatten to 1/2 inch thick using the bottom of a glass. If the dough is sticking to the glass, press the bottom of the glass in granulated sugar before flattening. Bake 8-9 minutes.
While cookies bake, stir all ingredients together for glaze until smooth.
Once cookies are finished baking, cool 3 minutes on baking sheet before transferring to cooling rack. Spread 1 1/2 teaspoons glaze over each warm cookie. Let glaze harden 2-3 hours before serving. OR eat them warm with lots of runny glaze :)