Bring tea to a boil in a 3-qt. saucepan over medium-high heat; stir in rice and 1/2 tsp. salt. Cover, reduce heat to low, and simmer 20 minutes or until tea is absorbed and rice is tender.
Meanwhile, melt butter in a large skillet over medium heat; add onion, and sauté 20 minutes or until caramel colored. Stir in balsamic vinegar, 1/4 tsp. salt, and pepper. Stir in hot cooked rice.