Prepare the rice according to the package directions.
Meanwhile, place the squash in a saucepan, cover with water, and boil until tender, about 5 minutes. Drain and set aside.
Heat half the oil in a skillet over medium heat. Add the eggs and cook, stirring, until they’re scrambled. Remove from the pan and set aside.
Add the remaining oil and the onion to the skillet and cook for 2 minutes. Add the coconut milk and simmer for 2 minutes.
Add the squash, rice, edamame, and ½ teaspoon salt and cook, stirring gently, until heated through and all the liquid is absorbed, about 2 minutes.
Remove from heat. Add the scallions and eggs, toss, and serve.