Preheat oven to 350 degrees Fahrenheit. Line a sheet pan with parchment paper.
Add oil, sugar, egg, molasses, and instant coffee to a large bowl and whisk to combine.
Add all remaining cookie ingredients (spices, baking powder + soda, salt, flour) and stir well to combine. Batter will be very thick.
Scoop batter onto prepared pan, dividing evenly into 9 cookies. I like to use a large cookie scoop or a 1/4 cup measuring cup to make sure they're all even. Use your fingers to press down slightly on each ball of dough, as they will not spread much whille baking.
Bake for 12-14 minutes, or until puffed and set in the center. They will still be quite soft in the middle at this point, which helps keep them from drying out once cooled!
Let cookies cool completely, then stir together all icing ingredients in a small bowl, and drizzle over the cookies. Eat immediately, or let the cookies dry for 10-15 minutes so the icing hardens. Leftovers keep well in an airtight container for 4-5 days.