Cook the rice. Rinse the rice under cold water until it runs mostly clear. Add rice, water, and a pinch of salt to a pot. Bring to a boil, then reduce heat, cover, and simmer until tender, about 12–15 minutes for jasmine.
Fluff with a fork and keep covered.
Make the teriyaki sauce base. In a small bowl or measuring cup, whisk soy sauce, water, maple syrup or brown sugar, rice vinegar, sesame oil, garlic, ginger, and optional chili sauce.
Thicken the sauce. In a separate small bowl, mix cornstarch with water to make a slurry. Pour the teriyaki base into a small saucepan over medium heat. Once steaming, whisk in the slurry and cook 1–2 minutes until glossy and thick enough to coat a spoon.
Remove from heat.
Prep the vegetables. Slice everything into bite-size pieces for even cooking. Keep firmer vegetables (carrots, broccoli) separate from quicker-cooking ones (snap peas, mushrooms, zucchini).
Stir-fry the veggies. Heat the oil in a large skillet or wok over medium-high heat. Add carrots and broccoli first; cook 2–3 minutes, stirring.
Add onion, bell pepper, and mushrooms; cook 3–4 minutes until crisp-tender. Add snap peas and zucchini for the final 1–2 minutes.
Sauce it up. Reduce heat to medium. Pour in enough teriyaki sauce to coat the vegetables, tossing until everything is shiny and heated through.
Reserve extra sauce for drizzling.
Assemble the bowls. Spoon rice into bowls, top with the saucy veggies, and finish with green onions, sesame seeds, and a squeeze of lime if using. Add more sauce to taste.