Preheat oven to 375°F.
Working in batches, cook green beans in a large pot of boiling salted water until bright green and halfway to tenderness, about 3 minutes per batch. Drain and let cool (pre snap the ends if you are using whole green beans).
Heat 1 Tbsp. oil in a large skillet over medium-high. Cook half of mushrooms, without stirring, until golden brown underneath, about 2 minutes. Toss occasionally and continue to cook, until browned on both sides, about 3 minutes more.
Add 2 tbsp. butter and 2 thyme sprigs to pan. Cook, tossing occasionally, until butter browns and mushrooms are dark brown and very tender, about 4 minutes longer. Season with salt and transfer to a plate.
Repeat with 2 tbsp. butter, salt, and remaining oil, other half of mushrooms, and thyme.
Melt remaining 2 tbsp. butter in a large saucepan over medium-low. Mix in flour and whisk until roux is golden brown and smells mildly nutty, about 4 minutes.
Whisk in milk, cream, and Colman’s Prepared Mustard. Increase heat and bring to a simmer, whisking often, and cook until sauce is thick and bubbling, about 5 minutes.
Remove from heat and whisk in garlic and Parmesan; season with salt and pepper to taste.
Arrange green beans and mushrooms in a 2-qt. baking dish. Pour sauce over (it may not look like enough, but it will get saucier as it bakes). Cover tightly with foil and bake until sauce is bubbling, 25–30 minutes.
Uncover and continue to bake until lightly browned on top and around the edges, 15–20 minutes longer. Top with fried onions and continue to bake just until onions are darker and fragrant, about 3 minutes.
Let sit 10 minutes to set before serving.