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

(While the onions bake, you can blanch the green beans—step 4.) 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. To bread the onion slices, you’ll want to use one hand for dry and one hand for wet. It helps things move a little quicker and easier. First, dip a few slices into the flour. Then into the egg mixture. And finally, give them a nice dunk into the panko and coat them well. Place onto baking sheet. Repeat with the rest of the onions. Bake onions until golden brown, about 20 minutes. Flip them twice during this time. Set them aside.

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 the green beans and boil for 5 minutes. Fill a large bowl with ice water and set near the sink. Drain the beans and immediately transfer them into the bowl of ice water to stop the cooking process. Drain again, and set aside.

Over medium-high heat, melt the butter in a large 10- to 12-inch ovenproof skillet. Add the mushrooms, 1 teaspoon salt, and the pepper. Cook, stirring occasionally, until the mushrooms begin to release some moisture—about 5 minutes. Add the garlic, stir, and cook for another 2 minutes. Sprinkle the flour on top and stir until combined. The flour will soak up all the moisture. Add the chicken broth and simmer for 3 minutes. Reduce the heat to medium-low and add the half-and-half. Stirring occasionally, cook until the mixture is thick—about 10 minutes or maybe more if you prefer a thicker sauce.

Remove from heat and add about a quarter of the onions, and all of the green beans. Give it a good stir, combining the sauce and beans. (If you’re not using an oven-safe skillet, or want to bake this in a casserole dish, transfer mushroom/gravy mixture to a greased 2–3-quart casserole dish.) Top with remaining onions and bake until bubbling around the edges, about 15 minutes. Remove from the oven and serve warm.

Leftovers keep well in an airtight container in the refrigerator for up to 4 days. Reheat as desired.