Preparation

• Preheat the oven to 450°F (232°C). Line a large baking sheet with parchment paper or a silicone baking mat. Set aside.
• Thinly slice the onion, and separate the slices. Pour flour in one small bowl, panko + salt + pepper into a medium bowl, and whisk the egg and milk together in another small bowl. Bread the onion slices by dipping them into flour, then into the egg mixture, and finally into the panko. Place onto the baking sheet. Bake until golden brown, about 20 minutes, flipping twice.
• Reduce oven temperature to 400°F (204°C).
• Blanch the green beans: Bring a gallon of water and 1 Tablespoon of salt to a boil in a large saucepan. Add green beans and boil for 5 minutes. Transfer beans to a bowl of ice water to stop cooking, then drain and set aside.
• In a large ovenproof skillet, melt butter over medium-high heat. Add mushrooms, 1 teaspoon salt, and pepper. Cook until mushrooms release moisture, about 5 minutes. Add garlic and cook for another 2 minutes. Sprinkle flour on top and stir until combined, then add broth and simmer for 3 minutes. Reduce heat to medium-low and add half-and-half, cooking until thick, about 10 minutes.
• Remove from heat and add about a quarter of the onions and all of the green beans. Stir to combine. If not using an oven-safe skillet, transfer to a greased casserole dish. Top with remaining onions and bake until bubbling, about 15 minutes. Serve warm.
• Leftovers keep well in an airtight container in the refrigerator for up to 4 days. Reheat as desired.