Cook udon noodles according to package instructions, about 5–7 minutes. Drain and set aside.
Heat 1/2 tbsp sesame oil in a skillet over medium-high heat. Add sliced chicken; cook until browned and cooked through, about 5–7 minutes. Remove from pan.
In the same skillet, add remaining sesame oil if needed. Toss in bell peppers and carrots; stir-fry for about 3–4 minutes until tender yet retain some crunch.
Return cooked chicken to the skillet with vegetables. Add udon noodles, soy sauce, and vegetable broth; stir until well coated and heated through.
Stir in minced garlic during the last minute of cooking. Remove from heat, garnish with green onions, and serve hot.
