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

Prepare the onion. Thinly slice it and separate the slices. Set up your breading station with bowls of flour, panko mixed with salt and pepper, and whipped egg with milk.

Dip each onion slice in flour first, then the egg mixture, and finally coat with panko. Place on the baking sheet and bake for about 20 minutes, flipping twice until golden brown.

Lower the oven temperature to 400°F (204°C). Boil a gallon of water with 1 Tablespoon of salt in a large saucepan.

Once boiling, add the fresh green beans and cook for 5 minutes. Transfer to a bowl of ice water to stop the cooking, then drain.

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

Add minced garlic and sauté for another 2 minutes. Sprinkle remaining flour, stir until combined, then pour in chicken broth and simmer for 3 minutes.

Lower heat to medium-low and mix in half-and-half, cooking until thick, about 10 minutes.

Combine the baked onions and prepared green beans in the skillet. Transfer to a greased casserole dish if necessary, top with remaining onions and bake until bubbling, about 15 minutes.

Remove from the oven and serve warm.