1. Measure 4 cups carrots.
2. Combine black beans, garlic, ginger, and red pepper flakes.
3. Combine sauce ingredients in small bowl, stirring to dissolve sugar.
4. Blend cornstarch and broth until smooth. Set aside.
5. Heat skillet over high heat. Add oil, swirling to coat pan., reduce heat to medium-high. Add black bean mixture and stir gently until fully fragrant, about 10 seconds.
6. Add carrots, drizzling in more oil if necessary. Cook about 1 minute.
7. Add sauce to pan. Cover pan and simmer 3-4 minutes until carrots are tender-crisp and still a bit underdone. Add extra splash of vinegar or a dash of sugar if need be.
8. Stir cornstarch and chicken broth mixture quickly to recombine and then add to pan. Cook 10 seconds. Remove to heated serving bowl and keep warm in 200-dregree oven.