Bring a large soup pot of water to a boil and cook the ramen noodles until tender, about 5–8 minutes; drain and set aside, discarding the seasoning packets.
In a large skillet over medium-high heat, add 1 tablespoon sesame oil. When hot, add snow peas, red pepper, broccoli, and onion; cook, stirring often, until the onions and peppers begin to soften, about 3–4 minutes. Remove the vegetables from the skillet and set aside.
Leave the skillet on medium-high heat and add the remaining 1 tablespoon sesame oil. When hot, add the cubed chicken, minced garlic, and grated ginger; cook, stirring, until the chicken is cooked through and no pink remains, about 5–7 minutes. Drain any excess liquid from the skillet.
Return the cooked vegetables to the skillet with the chicken. Add honey, soy sauce, rice vinegar, and crushed red pepper flakes; stir to combine and bring to a simmer.
Add the cooked ramen to the skillet and toss everything together until the noodles are evenly coated in the sauce and heated through, about 1–2 minutes.
Transfer to a serving dish and serve immediately.
