Whisk soy sauce, chicken broth, rice vinegar, cornstarch, ginger, honey, and garlic together in a small bowl; set aside.

Bring a pot of lightly salted water to a boil. Cook ramen noodles in the boiling water, stirring occasionally, until tender, about 3 minutes. Drain, reserving 1 cup of cooking water.

Heat sesame oil in a large skillet or wok over medium heat. Add scallions and carrots to the hot skillet and quickly stir-fry until soft, about 1 minute. Reduce heat to medium-low, pour in sauce, and cook until sauce starts to thicken, about 2 minutes. Stir in drained ramen noodles, separating and tossing them with tongs until coated. Add reserved cooking water a little at a time until you reach your desired consistency.