Preheat oven to 400 degrees F (200 degrees C). Press pie crust into a 9-inch pie dish.
Beat evaporated milk, brown sugar, coffee-flavored liqueur, corn syrup, cinnamon, salt, cloves, nutmeg, and ginger together in a bowl using a stand mixer fitted with the whisk attachment until smooth.
Pour pumpkin and eggs into brown sugar mixture; beat until well incorporated. Pour pumpkin mixture into pie crust.
Bake pie in the preheated oven for 10 minutes. Reduce heat to 325 degrees F (165 degrees C) and continue baking until center begins to firm, about 30 minutes.
