Whisk all sauce ingredients except the cornstarch slurry in a small bowl; set aside. Stir the slurry separately — cornstarch settles fast, so re-stir right before it goes in.
Heat a wok or large skillet over high heat until very hot; add the oil and swirl.
Firm vegetables first: add the carrot and broccoli. Stir-fry 2 minutes. Add a splash (1 tbsp) of water and cover 1 minute if the broccoli needs help — then uncover so the water evaporates.
Medium vegetables next: add the bell pepper and snap peas. Stir-fry 2 minutes.
Pour in the sauce (not the slurry yet) and toss to coat; bring to a simmer.
Re-stir the slurry, drizzle it in, and toss 1 minute until the sauce turns glossy and lightly thickens — it should coat the vegetables, not pool.
Serve immediately over rice, or as a side. Spoon any pan sauce over the top.