For the salad: Melt the butter in a large, heavy-bottomed skillet over medium-high heat. Add the mushrooms to the melted butter and cook, stirring occasionally, until they are golden brown and have released their moisture, about 6 minutes. Stir in the thyme, Worcestershire, celery, garlic and salt to taste. Cook until the garlic and thyme are aromatic and the celery is starting to brown on the edges, about 2 minutes. The celery should still be lightly crisp. Add more salt if desired. Take off the heat and spread on a sheet tray to cool.
Meanwhile, bring a medium pot of water to a boil. Set up a large bowl of ice water and line a sheet tray with a paper towel or kitchen towel. Generously season the boiling water with salt. Add the green beans and cook for 2 to 3 minutes. Remove with a spider or drain in a colander and transfer to the ice bath. Once cooled, transfer the green beans to the lined sheet tray and thoroughly pat dry.
For the creamy Parmesan dressing: Whisk together the yogurt, Parmesan, mayonnaise, sherry vinegar, 1/4 teaspoon salt and 1 teaspoon pepper in a large bowl. Refrigerate if not using immediately.
To assemble: To the bowl of dressing, add the green beans, mushroom mixture and romaine. Toss to combine and everything is fully coated. Transfer to a serving dish and top with the almonds and crispy fried onions. Serve immediately.