Season the skin side of the salmon fillets with salt. Set them aside.
Prepare the teriyaki sauce: In a small saucepan, combine soy sauce, cooking sake, mirin, and sugar. Heat over medium-low, stirring until the sugar dissolves. Remove from heat, let it cool, then transfer to a container for later use.
Pat the skin side of the salmon dry with kitchen paper. Lightly dust both sides of the fillets with flour.
In a sauté pan, heat oil over medium heat. Once hot, place the salmon fillets in the pan, skin-side down. Fry until the skin is crispy. Sear the sides briefly, then lay the fillets on their bottom side, cooking until they are 80% done. Remove from the pan and set aside.
Pour the teriyaki sauce into the same pan and reduce it over heat until it thickens into a glaze. Return the salmon to the pan, basting with the teriyaki glaze until fully cooked. Turn off the heat and leave the salmon in the glaze.
For the fried rice, heat oil in a large wok. Sauté the white parts of the scallion, ginger, and garlic until aromatic. Add carrots and stir-fry for 2-3 minutes.
Add edamame to the wok and stir-fry for a minute. Then incorporate the cooked rice, followed by the miso butter and MSG. Continue stir-frying until the rice is hot and well combined.
Finish the fried rice by stirring in the green parts of the scallion. Serve the fried rice with the teriyaki glazed salmon and a sprinkle of sesame seeds.