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1
Mix soy sauce, 1/4 cup vegetable oil, miso paste, brown sugar, white wine, and red pepper flakes together in a bowl to make marinade.
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2
Place salmon fillets in a shallow dish. Add enough marinade to cover, reserving the remaining marinade. Marinate in the refrigerator, about 10 minutes.
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3
Preheat oven to 450 degrees F (230 degrees C). Lightly oil a cast iron skillet or grill pan and place in the oven while it preheats. (A countertop induction oven can be used in place of the oven. Preheat on the medium-high grill setting.)
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4
Remove salmon from marinade, reserving the marinade, and place skin-side up on the hot cast iron skillet; cook until bottom of salmon is lightly browned, 2 to 3 minutes. Flip salmon and continue cooking until fish flakes easily with a fork, 8 to 10 minutes more. (For the countertop induction oven, add salmon to grill pan, reserving marinade, and cook, skin-side down, for 1 1/2 minutes. Flip salmon and cook until fish flakes easily with a fork, 2 1/2 to 3 minutes.)
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5
Pour reserved marinade into a saucepan and heat until boiling; remove from heat.
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6
Place potatoes in a large pot and cover with salted cold water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain and return potatoes to the pot.
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7
Heat milk and 2 tablespoons butter together in a saucepan; bring to a simmer. Pour milk mixture over potatoes, a few tablespoons at a time, and mash using a potato masher until potatoes are desired chunkiness.
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8
Heat olive oil in a large skillet over medium heat. Add green beans and garlic; cook and stir until beans turn bright green and are lightly browned in places, about 5 minutes; stir in 1 teaspoon butter, salt, and pepper.
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9
Serve mashed potatoes and green beans alongside salmon. Drizzle reserved cooked marinade over the top.
