Whisk the sauce: In a bowl, combine balsamic vinegar, chicken broth, 2 tablespoons olive oil, honey, Dijon, garlic, rosemary, thyme, 1 teaspoon salt, 1/4 teaspoon pepper, and red pepper flakes if using.
Taste and adjust sweetness or tang to preference.
Layer the crockpot: Add sliced onion to the bottom of the slow cooker. Place the chicken on top. Pour the balsamic mixture over the chicken, turning pieces to coat well.
Cook the chicken: Cover and cook on Low for 4–5 hours or on High for 2.5–3 hours, until the chicken is tender and reaches 165°F internally.
Thighs stay juicier than breasts if you can choose.
Prep the veggies: About 40 minutes before you plan to eat, heat the oven to 425°F. Toss potatoes, broccoli, carrots, and bell pepper with 1 tablespoon olive oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper on a large sheet pan.
Roast: Roast for 25–35 minutes, stirring once halfway. Potatoes should be golden and fork-tender, and edges of broccoli lightly charred.
Reduce the sauce (optional but great): When the chicken is done, transfer it to a plate and tent loosely with foil.
Pour the cooking liquid into a small saucepan. Simmer over medium heat for 8–10 minutes until slightly thickened and glossy. If you want it even thicker, whisk 1 teaspoon cornstarch with 1 teaspoon water and stir it in.
Cook 1–2 more minutes.
Finish and serve: Shred the chicken into large chunks or leave whole. Spoon some reduced balsamic sauce over the top. Plate with roasted veggies and more sauce.
Garnish with chopped parsley or basil.