Heat oil in a large nonstick skillet over medium-high heat. Add onion; cook for 1 minute. Cover, reduce heat to medium, and cook for 6 minutes or until soft. Stir in 1/4 cup honey and vinegar. Cook, uncovered, 10 minutes, stirring occasionally. Set aside.
While onions are cooking, place each chicken breast half between 2 sheets of heavy-duty plastic wrap, and flatten to 1/2-inch thickness using a meat mallet or a rolling pin. Combine mustard, 1 tablespoon honey, paprika, and salt in a small bowl. Brush half of mustard mixture over chicken. Heat a large grill pan or skillet coated with cooking spray over medium-high heat. Place the chicken, coated side down, in pan; cook for 4 minutes. Brush chicken with the remaining mustard mixture. Turn chicken over; cook 4 minutes or until done. Place 1 chicken breast on each toast slice, and top each with 2 tablespoons onion mixture.