Fill a heavy Dutch oven or cast iron pot with a few inches of cooking oil. Heat over medium-high until the temperature reaches 375°F. Line a sheet pan with paper towels.

In a medium-sized mixing bowl, combine the flour and beer to make a pancake-like batter (thick but still pourable), using more beer if needed. Toss the onions in the batter and mix to coat evenly. Add the onions to the hot oil and cook until fluffy and light golden brown. Remove onions using a spider or slotted spoon to the sheet pan. Season generously with salt and set aside.

Crispy onions can be made 2 days in advance; store in an airtight container.

Preheat oven to 350°F. Bring a large pot of salted water to a boil. Add beans and cook until deep green and tender, about 10 - 15 minutes. Drain and rinse with cool water.

In a large Dutch oven, melt 2 tablespoons of butter on medium-high heat. Add mushrooms and sauté until they start sweating liquid, about 4 minutes. Add onion, garlic, and a pinch of salt, cooking until softened, about 6 minutes. Add wine and simmer until it evaporates, about 3 minutes. Remove mushroom mixture to a separate bowl.

Combine milk, cream, and chicken stock in a bowl and microwave until hot, about 2-3 minutes. Melt remaining butter in the Dutch oven over medium-low heat. Add flour and whisk until creamy, about 2 minutes. Add the hot milk mixture and continue cooking, whisking frequently until thickened, about 15 minutes. Whisk in Worcestershire sauce, mustard powder, and generous salt and pepper.

Stir the mushroom mixture into the cream sauce and simmer for about 5 minutes, then taste and adjust seasoning.

Stir green beans into mushroom sauce and toss to combine. Pour mixture into a large buttered casserole dish. Bake uncovered for 15 minutes.

Add grated cheddar and crispy onions on top; bake until cheese is melted, about 15 more minutes. Let stand for 10 minutes before serving.