Whisk all sauce ingredients in a small bowl until the starch fully dissolves and no lumps remain. Set near the stove.
Heat a large skillet or wok over medium-high. Add 1 tablespoon oil. Pat salmon dry, season lightly with a pinch of salt, and sear in a single layer for 1 to 1 1/2 minutes per side until just turning opaque at the edges. Transfer to a plate (it will finish cooking in the sauce).
Add the remaining 1 1/2 tablespoons oil to the pan. Stir-fry the shallot for 45 seconds. Add carrot and bell pepper; cook 2 minutes. Add broccoli and a pinch of salt, splash in 2 tablespoons water, cover, and steam 2 minutes. Uncover and stir-fry 1 minute more until crisp-tender.
Return salmon and any juices to the pan. Give the sauce a quick stir (starch settles fast) and pour it in. Reduce heat to medium and toss gently until the sauce thickens and turns glossy, 1 to 2 minutes; the salmon should be just cooked through.
Remove from heat and drizzle with toasted sesame oil. Taste and adjust with a pinch of salt or a splash of water if the sauce is too thick. Sprinkle with scallions and sesame seeds and serve hot over rice or noodles.