In a small bowl, combine the spices for the chai spice mix and sugar. Mix with a spoon and set aside.
In a medium bowl, combine the all-purpose flour, all of the spices in the cookie ingredient section, baking soda and salt. Set aside. In the bowl of a stand mixer, fitted with a paddle attatchment, add the butter and sugar. Mix on medium speed until light and fluffy, at least 5 minutes, scraping down the sides of the bowl with a nonstick spatula half way through. Add in the molasses and corn syrup, mix again. Add in the egg and mix until smooth. Add in the dry ingredients and mix until thick dough forms. Remove dough from the mixing bowl and divide in half. Pat each half into a disc and cover in cling wrap. Chill in the refrigerator for at least 4 hours.
Preheat oven to 350F. Take dough out of the refrigerator, and place onto a floured surface. Roll out into a ⅓” thickness. Cut out cookies into desired shape and sprinkle the chai spice on top of each one before baking. Bake for 9 minutes. Remove from oven and let cool while you make the frosting.
In a medium bowl, add the melted butter and the espresso powder, mix with a spoon or nonstick spatula to dissolve the espresso granules. Then add in the powdered sugar, heavy cream, and salt. Mix again with a nonstick spatula or with a handmixer on low speed until smooth frosting forms. Frost cookies as you wish!