Combine 1 tablespoon sake, mirin, sugar and soy sauce and mix well until the sugar is mostly dissolved. Set aside.
Rinse the salmon and pat dry. Season the salmon with salt and black pepper on both sides.
Sprinkle half of the flour on one side of salmon and spread evenly. Turn fillets over and sprinkle on the rest of flour.
In a frying pan, add the olive oil and melt the butter over medium heat. Don’t burn the butter. If the
flying pan gets too hot, reduce heat or remove from the heat temporally.
Add the salmon fillets, skin side on the bottom. Cook the salmon for 3 minutes, or until the skin is nicely browned.
Add 1 tablespoon sake and cover with lid. Steam the salmon for 3 minutes, or until it's cooked through. Remove the salmon to a plate.
Add the reserved sake mixture to the pan and heat up. When the sauce starts to boil, add salmon back in the pan and spoon the sauce over the salmon.
When the sauce thickens, turn off the heat. Plate the salmon and serve immediately.