Season chicken with salt and pepper; brown in olive oil over medium-high heat 3 minutes per side.
Put mushrooms, onion, and garlic in a 6-quart slow cooker; lay chicken on top.
Whisk broth with 1/4 cup balsamic and Worcestershire; pour around chicken.
Cover; cook on low 3 1/2 to 4 hours until breasts reach 165°F.
Transfer chicken to a board; slice across grain.
Whisk cornstarch and cold water; stir into mushroom liquid. Cook on high 8 minutes.
Stir in remaining balsamic; return sliced chicken just long enough to coat.