Prep the sauce: In a small bowl, whisk soy sauce, mirin, brown sugar (or honey), and rice vinegar until the sugar dissolves. In another small bowl, stir together cornstarch and water to make a slurry.
Set both aside.
Cook the noodles: Boil noodles according to package directions until just tender. Drain and rinse briefly with cool water to stop cooking. Toss with a few drops of sesame oil to prevent sticking.
Prep the salmon: Pat salmon dry and season lightly with salt and pepper.
Cut into 1-inch pieces so they cook quickly and stay moist.
Sear the salmon: Heat a large skillet or wok over medium-high heat. Add 1 tablespoon oil. Place salmon pieces in a single layer and sear 2–3 minutes per side until just cooked through and lightly browned.
Remove to a plate.
Stir-fry the veggies: In the same pan, add a splash more oil if needed. Add broccoli (or snap peas), bell pepper, and carrot. Stir-fry 2–3 minutes until crisp-tender.
Add aromatics: Add garlic and ginger.
Stir for 30 seconds until fragrant. Don’t let them brown.
Build the sauce: Pour in the teriyaki mixture and bring to a gentle simmer. Stir in the cornstarch slurry and cook 30–60 seconds until glossy and thick enough to coat a spoon.
Toss noodles and salmon: Add the noodles to the pan and toss to coat.
Gently return the salmon and fold it in so it stays flaky but intact. If the sauce feels too thick, splash in a tablespoon of water.
Finish: Turn off the heat. Stir in scallions and a drizzle of toasted sesame oil.
Taste and adjust with more soy for salt, a pinch of sugar for sweetness, or a squeeze of lime for brightness.
Serve: Plate the noodles and salmon. Sprinkle with sesame seeds and optional red pepper flakes. Serve with lime wedges.