1. Cook barley in a large pot of boiling water for 35 minutes or until tender-chewy. Drain.
2. While barley cooks, place rice in a small saucepan; cover with water to 2 inches above rice. Swirl rice with hand in pan to agitate; drain. Repeat procedure 2 more times. Add 2/3 cup water to drained rice in pan. Bring to a boil over medium-high heat. Cover, reduce heat, and simmer 15 minutes. Remove from heat; let stand 10 minutes. Combine rice and barley in a large bowl.
3. Heat a medium nonstick skillet over medium-high heat. Add 1 teaspoon oil to pan; swirl to coat. Add carrot; sauté 2 minutes or until crisp-tender. Remove from pan. Add 1 teaspoon oil and zucchini to pan; sauté 1 minute or until crisp-tender. Remove from pan. Add 1 teaspoon oil and mushrooms to pan; sauté 2 minutes or until tender. Remove from pan. Add 1 teaspoon oil and bean sprouts to pan; sauté 1 minute or until bean sprouts wilt. Remove from pan. Add remaining 1 teaspoon oil and spinach to pan; sauté 1 minute or until spinach wilts. Arrange vegetables in separate piles over rice mixture. Dollop with miso and gochujang; top with microgreens. Sprinkle with sesame seeds. Mix together at the table.