In a small bowl, whisk together the balsamic vinegar, honey, brown sugar, and cornstarch until well combined. This will be the glaze that adds flavor and moisture to the chicken.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Season the chicken breasts with salt and pepper. Once the oil is hot, add the chicken to the skillet. Sear for about 4-5 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining tablespoon of olive oil. Toss in the broccoli florets and sugar snap peas. Sauté the vegetables for about 3-4 minutes, or until they are tender-crisp. If needed, add water to help steam the vegetables.
Return the chicken to the skillet and pour the balsamic glaze over the chicken and vegetables. Gently stir to coat everything evenly in the sauce. Allow it to simmer for an additional 2-3 minutes, letting the glaze thicken slightly.
Once everything is heated through and well-coated, remove from heat. Serve the One-Skillet Balsamic Chicken and Vegetables warm, perhaps over a bed of rice or quinoa for a complete meal. Enjoy the delightful combination of flavors!
