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Step 1
For the onion topping: Preheat the oven to 350 degrees F.
Step 2
Combine the onions and milk in a bowl, then set aside.
Step 3
Heat 2 inches oil in a high-sided heavy-bottom pot to 375 degrees F.
Step 4
In a bowl, combine the flour and seasoning salt. In batches, lightly dredge the onions in the flour, shaking off the excess. Drop into the oil and fry util golden and crisp, about 1 minute. Remove each batch to a paper towel-lined sheet pan.
Step 5
For the casserole: Blanch the green beans by dropping them into lightly salted boiling water, allowing the green beans to cook for 3 to 4 minutes. Remove them with a slotted spoon and immediately plunge them into a bowl of ice-cold water to stop the cooking process. Drain the beans once they're cool, then set aside.
Step 6
Make the sauce by adding the olive oil and 2 tablespoons butter to a large skillet over medium-high heat. Add the mushrooms, onions, garlic and rosemary. Cook, stirring frequently, until the mushrooms have released their moisture and started to brown and the onions have softened, 5 to 6 minutes. Season with a good pinch of salt and pepper. Add the remaining 2 tablespoons butter and let it melt. Sprinkle over the flour and stir to make a roux, letting it cook for about 2 minutes. Slowly stir in the stock and cream. Let cook slightly to thicken, 5 to 6 minutes. Taste and adjust the seasoning as needed.
Step 7
In a large baking dish, add half the blanched green beans. Top with half the sauce, then the remaining green beans and the remaining sauce. Top with the Parmesan, then bake until it has melted and the sauce is bubbling, about 20 minutes. Let sit for a few minutes before mounding the top with the fried onion topping and sprinkling over the parsley. Serve.