In a small bowl, whisk together the soy sauce, rice vinegar, honey, Sichuan chili crisp, garlic, ginger, and water until smooth.
Heat 1 tablespoon of cooking oil in a large skillet over medium-high heat. Add the chicken and cook for 4 to 6 minutes, stirring occasionally, until browned and cooked through. Transfer to a plate.
In the same skillet, add the remaining 1 tablespoon of cooking oil, followed by the cabbage and carrot. Cook for 2 to 3 minutes until wilted and lightly browned. Add the scallion whites and cook for another minute.
Add the noodles to the skillet and toss well.
Return the chicken to the pan, add the scallion greens, and pour in the sauce. Toss everything together until the noodles are coated and heated through, 1 to 2 minutes.
Serve with extra chili crisp, sesame seeds, or scallion greens if desired.