First, prepare the marinade for the fish. Combine the marinade ingredients in a mixing bowl large enough to hold all the salmon belly pieces. Stir until brown sugar is completely dissolved.
Put the fish in the bowl. Stir and make sure all the pieces are covered with the marinade. Cover the bowl with a plastic wrap and let the fish sit in the marinade for half an hour in the fridge.
In the meantime, cut and prepare the vegetables.
Place a large skillet or a wok on the stove. Heat in a medium-high setting. Add 1 tablespoon of the canola oil to the pan. Heat until the oil becomes smokey.
Add the marinated salmon pieces (reserving the marinade) to the pan. Stir-fry the salmon for about 2-3 minutes or until it's lightly browned. Remove the salmon pieces from the pan and set it aside on a plate.
In the same pan, add the remaining oil. When the oil is heated, put the minced garlic and grated ginger, and stir-fry for about 30 seconds or until fragrant.
Add the remaining vegetables to the pan. On medium-high heat, stir-fry the vegetables for 3-4 minutes or until they become tender-crisp.
Pour the reserved marinade over the vegetables and stir to coat them evenly.
Return the cooked salmon to the pan and shake the pan to make sure the salmon and the vegetables are well combined and heated through.
Divide the dish into serving plates. Garnish each plate with green onions and sesame seeds.