Preheat the oven to 450 degrees F. Mix the soy glaze with the rice vinegar and garlic. Divide the sauce between 2 small bowls and add 2 tablespoons water to one bowl; set aside.
Season the chicken with salt and pepper. Heat the vegetable oil in a large ovenproof nonstick skillet over medium-high heat. Add the chicken skin-side down and cook until the skin is golden and crisp, about 6 minutes. Flip and cook until golden on the other side, about 4 more minutes. Pour the thinned soy glaze mixture over the chicken. Transfer to the oven and bake, 10 minutes.
Meanwhile, combine the vegetables, 2 tablespoons water and 1/2 teaspoon salt in a microwave-safe bowl; cover loosely with plastic wrap. Microwave until tender, about 4 minutes. Stir in 1 tablespoon of the remaining soy glaze mixture.
Remove the chicken from the oven; brush with the remaining soy glaze mixture. Return to the oven and bake until the chicken is cooked through, about 5 minutes. Serve with the vegetables and rice.