Mocha donuts Spiked

Name: Mocha donuts Spiked
Cuisine: American
Ingredients: 2 cups all-purpose flour; 1 teaspoon baking powder; 1/2 teaspoon baking soda; 1/2 teaspoon kosher salt; 1/2 cup granulated sugar; 2 tablespoons unsalted butter, room temperature; 1 large egg, room temperature; 1/3 cup rumchata; 2 tablespoons instant coffee; 2 quarts canola oil (for frying); 1 stick (½ cup) salted butter, softened; 1 tbsp instant coffee; 1 lb powdered sugar (about 4 cups); 1 tsp vanilla extract; 4 tbsp Kahlua; 1 tbsp dark chocolate syrup; Chocolate sprinkles