Preheat the broiler, ina medium ovenproof pan toss the shrimp with 1 teaspoon each of the sesame oil, honey. Add the cayenne.
Lay the shrimp flat. Broil for 2 minutes per side. Transfer to a plate.
Heat a small nonstick skillet over medium heat and add the remaining teaspoon of sesame oil. Pour in the eggs. Cook undisturbed until set, about 2 minutes. Flip and cook until just set on the other side, about 1 miunte. Transfer to a board and cut into strips.
In a small bowl combine the soy sauce and rice wine vinegar with the remaining 1/2 teaspoon honey.
Fold the edamame and sesame seeds into the rice. Serve the rice in bowls topped with the egg strips, shrimp and avocado. Place the soy dressing as a side for drizzling.