Whisk together all ingredients for the teriyaki sauce until evenly combined. Alternatively combine everything in a jar with a tight-fitting lid and shake well. (Note: you will need to whisk or shake extra well to eliminate any cornstarch lumps.)
While cooking the stir-fry in the next steps, cook soba noodles (or rice) according to package directions.
Pat the salmon cubes dry with paper towels and then season lightly with salt and pepper. Set aside. (Note: It is a good idea to let the salmon come up a couple of degrees out of the fridge. Very cold fish will have a tendency to stick to the pan more than less cold fish. However, if the fish will sit out for more than 10 minutes or so, it’s best to keep it in the fridge to maintain a safe temperature.)
Heat a large nonstick pan or wok over medium-high heat.
Add 2 Tablespoons cooking oil to the heated pan and then broccoli florets. Cook broccoli florets, stirring occasionally, until browning in spots, about 5 minutes.
Pour water over broccoli and cover pan with a lid. Steam broccoli, covered, until tender but still crisp, 3 to 4 minutes.
Remove broccoli florets from the pan and set them aside near the stove.
Return pan to heat and let any excess water cook off.
Reduce to medium. Add 2 Tablespoons cooking oil. When oil is hot, add salmon and cook on one side until golden brown. Gently flip salmon to cook on all sides until nearly cooked through, 3 to 5 minutes total.
Pour sauce over salmon and bring to a simmer. Simmer for 1 minute until sauce thickens and coats salmon.
Add broccoli to pan and gently fold everything together.
Serve stir-fry over noodles with sesame seeds on top.