Preheat the oven to 450°F (232°C). Line a large baking sheet with parchment paper or a silicone baking mat.

Thinly slice the onion, and separate the slices. Pour flour in one small bowl, panko, salt, and pepper into a medium bowl, and whisk the egg and milk together in another small bowl.

To bread the onion slices, use one hand for dry and one hand for wet. First, dip a few slices into the flour, then into the egg mixture, and finally coat them well with the panko. Place onto the baking sheet.

Bake onions until golden brown, about 20 minutes, flipping them twice during this time. Set aside.

Bring a gallon of water and 1 Tablespoon of salt to a boil in a large saucepan. Add the green beans and boil for 5 minutes.

Transfer the beans into a bowl of ice water to stop the cooking process. Drain and set aside.

Over medium-high heat, melt the butter in a large ovenproof skillet. Add the mushrooms, 1 teaspoon salt, and the pepper. Cook until mushrooms release moisture, about 5 minutes.

Add garlic and cook for another 2 minutes. Sprinkle the flour on top and stir until combined.

Add the chicken broth and simmer for 3 minutes. Reduce the heat and add half-and-half. Cook until the mixture thickens, about 10 minutes.

Remove from heat and add a quarter of the onions and all of the green beans. Stir to combine. Transfer to greased casserole dish if skillet is not oven-safe.

Top the casserole with remaining onions and bake until bubbling, about 15 minutes.

Remove from oven and serve warm.