How to Make It
In a skillet, boil the wine and shallot over moderately high heat until reduced to 1/4 cup, 10 minutes. Reduce the heat to moderate. Gradually add the butter to the skillet and whisk constantly on and off the heat until the sauce is creamy. Remove from the heat and whisk in the miso and soy sauce; season with salt and pepper.
Light a grill or heat a grill pan. Brush the cod fillets with oil and season with salt and pepper. Brush the grill with oil and cook the fish over high heat, turning once, until lightly charred and just cooked, 4 to 5 minutes.
In a large skillet, heat 1 teaspoon of the oil until shimmering. Add the lettuces and toss over high heat until barely wilted, about 30 seconds. Transfer the lettuces to plates and top with the fish. Briefly rewarm the sauce, whisking, over moderate heat. Spoon some of the sauce over the fish and serve. Pass the remaining sauce separately.