Rinse chicken and pat dry. Place each breast half between 2 sheets of plastic wrap and pound with a flat-surfaced mallet to a thickness of 1/3 to 1/2 inch. Lay a slice of capocollo on each pounded chicken piece, pressing lightly so that chicken and sausage stick together. Set aside.
Heat oil in a wide frying pan over medium heat. Add onions and garlic; cook, stirring often, until vegetables are lightly browned (about 3 minutes). Then push vegetables to one side and place chicken in pan. Cook just until edges of chicken pieces begin to brown on bottom (about 4 minutes). Turn pieces over and continue to cook until meat in thickest part is no longer pink; cut to test (3 to 4 more minutes). Transfer chicken, sausage side up, to a platter; keep warm.
To pan, add broth, mustard, lemon juice, and basil. Bring to a boil over high heat, stirring constantly; then pour broth mixture over chicken.