Preheat sandwich press according to manufacturers' instructions.
Heat oil in a skillet over medium heat. Add chicken; cook, turning halfway through, until no longer pink in the center and the juices run clear, about 10 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Transfer to a plate.
Place bacon in a separate skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels.
Spread 1 tablespoon butter over the outside of each slice of bread. Spread mayonnaise over 2 bread slices; assemble chicken, bacon, Cheddar cheese, tomato, and sprouts on top. Cover with the remaining 2 slices, buttered side-up. Place sandwiches into the sandwich press; cook until cheese is melted and bread is toasted, 5 to 8 minutes.