Start by heating 1 tablespoon of olive oil in a large skillet over medium-high heat. Season your chicken pieces with salt and pepper, then place them in the hot skillet. Sear each side for 3-4 minutes until they're beautifully browned and fragrant. Transfer the seared chicken to the slow cooker.

In the same skillet, add another tablespoon of olive oil if needed. Sauté the diced onion over medium heat until it softens and turns translucent, about 3-4 minutes. Stir in the minced garlic and balsamic vinegar, and cook for another minute until aromatic.

Pour the aromatic onion and garlic mixture over the chicken in the slow cooker. Add the canned diced tomatoes, chopped green bell pepper, and sliced mushrooms. Sprinkle the Italian seasoning evenly across the mixture.

Cover the slow cooker and set it to HIGH for about 1.5-2.5 hours if using chicken breasts, or LOW for 4-5 hours if using thighs. Ensure the internal temperature reaches 165°F.

Consider uncovering the slow cooker and cooking on HIGH for an additional hour to thicken the sauce further. Stir in the remaining balsamic vinegar before serving.

Transfer the tender chicken and sauce over pasta, rice, or zucchini noodles. Garnish with fresh parsley and Parmesan cheese if desired.