In a large skillet, add oil, scallions and garlic. Stir fry them until soft and fragrant.
Add mushrooms. Cook until brown and caramelized.
Add edamame and bell peppers. Cook for 2 minutes.
Mix together all the ingredients for the sauce. Pour over the mushroom mixture. Stir until combined.
Boil the noodles according to the package. Before discarding the water, add 2 to 3 tablespoons of pasta water to the mushroom mixture. (This helps to thicken the sauce.)
Drain noodles, and add them to all the veggies.
Garnish with sesame seeds and scallions. Serve immediately.