Cook the udon noodles according to package directions. Drain and set aside.
In a bowl, whisk together 1/2 cup tamari or soy sauce, 3–4 tablespoons chili paste, 2 tablespoons rice vinegar, 2 tablespoons lemon juice, 2 tablespoons honey, 1 tablespoon toasted sesame oil, 6 cloves chopped garlic, and 1 tablespoon fresh chopped ginger. Set the sauce aside.
Heat a large skillet or wok over medium-high heat. Add the remaining 1 tablespoon toasted sesame oil to the pan.
Add 1 pound thinly sliced chicken breasts/thighs or ground chicken to the hot skillet. Cook, stirring or turning as needed, until the chicken is cooked through (about 4–6 minutes for thin slices; 6–8 minutes for ground), breaking up the ground chicken if using.
Add 2 cups frozen stir-fry veggies to the skillet and cook 2–3 minutes, stirring, until the vegetables are heated through but still slightly crisp.
Pour the prepared sauce into the skillet and add 1/4 cup chopped scallions. Stir, bring to a low simmer, and cook 1–2 minutes so the sauce heats and flavors the chicken and vegetables.
Add the cooked udon noodles to the skillet. Toss or stir gently for 1–2 minutes until the noodles are heated through and the sauce coats the chicken and noodles evenly.
Serve warm, topped with 2 tablespoons toasted sesame seeds and 1/4 cup fresh chopped cilantro or Thai basil.
Notes
Use tamari or soy sauce interchangeably.
Adjust chili paste amount (3–4 tablespoons) to taste.