Whisk balsamic, broth, honey, soy sauce, garlic, Italian seasoning, red pepper, salt, and black pepper in a bowl.
Drizzle the slow cooker with olive oil. Scatter onions on the bottom, then nestle in the chicken.
Pour the balsamic mixture over the chicken. Cover and cook on LOW 4–5 hours, until the chicken is tender.
Stir cornstarch with water to make a slurry. Switch cooker to HIGH and stir in the slurry.
Cook uncovered 10–15 minutes, until the sauce thickens and turns glossy. Slice or shred chicken and toss with sauce.
Finish with parsley and serve hot with extra sauce spooned over the top.