Step 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.
Step 2
Place salmon fillets in a shallow dish. Add enough marinade to cover reserving the remaining marinade. Marinate in the refrigerator about 10 minutes.
Step 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.)
Step 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.)
Step 5
Pour reserved marinade into a saucepan and heat until boiling; remove from heat.
Step 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.
Step 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.
Step 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.
Step 9
Serve mashed potatoes and green beans alongside salmon. Drizzle reserved cooked marinade over the top.