In a medium-sized bowl, combine all the patty ingredients and form 2 patties. Press patties in panko to coat. In a frying pan, heat oil over medium-high heat. Gently place patties in pan and brown on both sides, keeping the inside of the patties medium-rare.
In a separate saute pan, add the butter and mushrooms and saute for 2 minutes. Add remaining ingredients and cook 1 minute.
In a bowl, place a scoop of rice, 1 poke patty and pour enoki mushroom sauce on top. Sprinkle with minced green onion.