Melt butter in a small saucepan over medium heat. Add shallots, ginger, chile paste, and garlic; cook 3 minutes, stirring frequently. Add wine and mirin; bring to a boil. Cook until reduced to 3 tablespoons (about 8 minutes); remove from heat. Stir in miso.
Heat vegetable oil in a large nonstick skillet over medium-high heat. Sprinkle tuna steaks with salt and pepper. Add tuna to pan; cook 3 minutes on each side until fish is medium-rare or desired degree of doneness. Serve tuna steaks with sauce.