Preheat the oven to 350°F. Lightly grease baking sheets.
Combine flour, starches, cinnamon, baking soda, salt, and xanthan gum in a medium bowl; set aside.
In a large bowl, beat butter, brown sugar and granulated sugar until light and fluffy, about 2 minutes. Add pumpkin and vanilla extract and mix well. Add flour mixture and mix well. Stir in oats and cranberries.
Using a small cookie scoop, drop dough 2 inches apart on prepared baking sheets. Bake for 14-16 minutes or until light brown. Cool on baking sheets for a few minutes; transfer to wire racks and let cool completely.
To make the icing, whisk together all ingredients until smooth. If necessary, add more sugar to thicken or more water to thin the icing.