Preheat oven to 400°F
Bring a gallon and 1 tablespoon of salt to a boil in a large pot. Add the green beans and blanch for 3 minutes. Drain immediately and rinse with ice cold water to prevent them from continuing to cook.
Meanwhile, melt 2 tablespoons of the vegan butter in a large sauté pan over medium heat. Add the mushrooms and cook, stirring often, until most of the moisture cooks out, 6 to 8 minutes.
Add the remaining tablespoon of butter to the pan. Once it's melted, add the parsley, shallot, garlic, nutmeg, pepper, and white wine, and continue to cook, stirring often, until most of the wine evaporates, 3 to 5 minutes.
Sprinkle the flour over the mixture and stir to combine. Cook for 1 minute. Whisk in the non-dairy milk and broth and simmer until the mixture thickens, stirring occasionally, 8 to 10 minutes. Taste and adjust seasonings if necessary. Add the blanched green beans back into the pan and mix to combine. Remove from the heat and stir in 1 cup of the crispy onion strings. Transfer the mixture to a 9x13 prepared dish and bake until bubbly, 12 to 15 minutes. Top the casserole with the remaining onion strings and bake until the onion strings are dark and slightly crisped around the edges, 3 to 5 minutes. Garnish with fresh minced parsley and enjoy!