Preheat your oven to 350°F (175°C). Lightly grease a 13x9-inch baking dish and set aside.
In a large skillet, heat olive oil over medium heat. Sauté the mushrooms and onions until softened and slightly golden, about 7-10 minutes.
Add the minced garlic to the skillet, stirring continuously for 1 minute until aromatic.
Stir in the dairy-free sour cream, browning sauce (if using), salt, and pepper. Cook for 2 minutes, then remove from heat.
In a large bowl, combine the thawed green beans and shredded dairy-free cheese. Pour the sour cream mixture over the top and stir until coated.
Transfer the green bean mixture to the prepared baking dish and spread out evenly.
In a small bowl, melt the dairy-free buttery spread. Add the crushed crackers and chopped french-fried onions; mix until evenly coated.
Sprinkle the cracker mixture over the casserole, covering it completely.
Bake for 25-30 minutes or until the top is golden brown and the casserole is bubbly. Serve hot!