Mix the chicken, mayonnaise, scallions, smoked paprika and bacon until the pieces are evenly coated.
Place 1 cheddar slice on each of 4 bread slices and divide the chicken salad over the cheese.
Add the remaining cheddar and bread, then butter the outside of each sandwich.
Cook in a covered skillet over medium-low heat for 4 to 5 minutes on the first side.
Turn and cook for 4 to 5 minutes more until both sides are browned, the cheese melts and the center of the filling reaches 165°F.
Rest for 2 minutes before cutting so the filling stays inside.