Preheat your oven to 400°F (200°C). Line a large rimmed sheet pan with parchment paper or foil, making sure the liner comes up slightly on the sides to catch dripping glaze.
In a small saucepan over medium heat, whisk together soy sauce, honey, rice vinegar, sesame oil, garlic, and ginger; bring to a gentle simmer for 2 to 3 minutes. Whisk the cornstarch with the cold water until smooth, pour into the saucepan, and stir continuously for 1 to 2 minutes until the sauce thickens enough to coat a spoon.
Remove the sauce from heat and divide it: pour two-thirds into a bowl for marinating and basting the chicken, and reserve the remaining one-third in the saucepan to use as a finishing glaze at the end of roasting.
Pat the chicken thighs completely dry with paper towels, then season both sides with salt and black pepper. Toss the chicken in about half of the roasting-portion of sauce until fully coated, and let it sit while you prep the vegetables.
Combine broccoli florets, red bell pepper strips, zucchini half-moons, and snap peas in a large bowl. Drizzle with olive oil, season with salt and black pepper, and toss until every piece is evenly coated.
Spread the vegetables in a single layer across the prepared sheet pan, leaving space between pieces. Nestle the sauced chicken thighs skin-side up on or beside the vegetables, then brush the remaining roasting-portion sauce over the chicken for an extra coat.
Roast on the center rack at 400°F for 25 minutes, undisturbed. Avoid opening the oven door to maintain consistent heat.
Remove the pan from the oven and generously brush the reserved finishing glaze over the chicken thighs. Return the pan to the oven and roast for another 5 to 7 minutes, until the glaze is caramelized and a meat thermometer reads 165°F (74°C) in the thickest part of the chicken.
Allow the chicken to rest on the pan for 5 minutes, then sprinkle with sesame seeds and sliced green onions. Serve immediately over steamed rice or noodles.