In a small bowl, whisk together 1/4 cup low-sodium soy sauce, 1 tablespoon honey, 1 teaspoon cornstarch, and 1/4 cup water until smooth; set the sauce aside.
Heat 2 tablespoons olive oil in a large skillet or wok over medium-high heat.
Add the 1 lb chicken pieces to the hot skillet, season with salt and pepper, and cook, stirring occasionally, until browned and nearly cooked through, about 5 to 7 minutes.
Increase the heat to high and add the minced garlic, minced ginger, 1 cup broccoli florets, sliced red and yellow bell peppers, and the thinly sliced carrot to the pan.
Stir-fry the vegetables with the chicken for 3 to 4 minutes, until the vegetables are crisp-tender.
Pour the reserved sauce over the chicken and vegetables, stir to combine, and cook for 2 to 3 more minutes until the sauce thickens and the chicken is cooked through.
Taste and adjust salt and pepper if needed, then serve immediately.