Rub the chicken with olive oil, paprika, salt and black pepper and let it stand for 15 minutes.
Divide the barbecue sauce between a 1/4-cup bowl for brushing and a separate 1/4-cup bowl for the finished sandwiches.
Heat a grill or grill pan to medium-high and brush the onion rings lightly with oil from the seasoned chicken bowl.
Grill the chicken and onion for 4 minutes, turn both and cook for 3 minutes more.
Brush the chicken with barbecue sauce, cook for 1 minute, turn and brush again.
Top each cutlet with cheddar, cover the grill and cook for 1 to 2 minutes, until the cheese melts and the chicken reaches 165°F; remove the onion when tender and browned.
Rest the chicken for 4 minutes, toast the pretzel buns and assemble each with 1 cheesy cutlet, 1 tablespoon reserved clean barbecue sauce and 1 grilled onion ring.