Preheat the broiler and line a baking sheet with foil. Place salmon skin-side down on the sheet, discarding the marinade. Broil for 7-8 minutes, or until the salmon flakes easily with a fork.
While the salmon cooks, pour the remaining sauce into a small saucepan over medium heat. In a small bowl, whisk 2 tsp cornstarch into 1 tbsp warm water, then stir this slurry into the sauce. Simmer for 2-3 minutes until thickened.
To assemble, place ¾ cup cooked rice into each bowl. Top with salmon, cucumber, edamame, and carrots. Add ¼ avocado onto one serving, then drizzle with half the sauce. Sprinkle with green onion and sesame seeds. Squeeze lemon over the remaining avocado to keep fresh for the next day's portion.