Heat non-stick frying pan on medium heat and add all ingredients but carrots in pan and stir. Add carrots into the pan and cover.
Cook on medium heat until carrots are soft, about 25 minutes. Monitor liquid levels as carrots cook and ensure liquid doesn't evaporate faster than carrots soften. Toward the end of the 25 minutes remove the cover and loosen fond and mix in with the carrots. Recover until carrots are finished cooking.
Carrots are finished with they can be easily pierced with a fork. Pour carrots into serving dish. If desired, scoop out any remaining sauce from the pan and drizzle over carrots. Serve with chives and lemon slices.