Preheat oven to 350 degrees F.
In a dry, large, enamel-coated, or similar skillet, add the sliced mushrooms and cook over medium heat until all the water from the mushrooms has been released, approximately 10 minutes. Turn the heat up when a lot of water has been released, and the higher heat will allow the water to evaporate faster. Stirring as needed and adjusting the heat so mushrooms do not become too dry in the skillet.
Lower the heat to medium. Make an open circle in the center of the skillet and add the butter, stir it to coat the mushrooms.
Season with kosher salt and black pepper.
Make an open circle in the center of the skillet and add the olive oil. Add the diced onions and minced garlic to the center of the skillet, stir to incorporate the onions and mushrooms together.
Add the white wine to the skillet and stir. Cook for a couple of minutes.
In a lightly oiled 1.5-quart baking dish, add half of the cooked mushrooms to the bottom. Sprinkle with half of the cheese and then half of the panko.
Add the balance of the cooked mushrooms to the baking dish. Top with the rest of the panko, and then top with the balance of the shredded cheese.
Bake uncovered in a preheated oven for 30 minutes, and if desired, turn on the broiler for the last 2 minutes to give the top of the mushroom a golden color.