Bring coffee-flavored liqueur to a simmer in a small saucepan over medium heat. Simmer until liqueur is reduced by half, 5 to 10 minutes.
Set oven rack in the middle of the oven and preheat the oven's broiler.
Place a slice of Chihuahua cheese on the back of each shrimp and wrap shrimp and cheese with 1 bacon strip; set on a baking sheet. Repeat for remaining shrimp.
Broil on the middle rack in the preheated broiler until bacon cooks and cheese melts, about 5 minutes.
Transfer cooked shrimp to a plate and drizzle with liqueur reduction.
