Preheat the oven to 350°F (175°C).
Cook the egg noodles according to package instructions until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add the chopped onion and sauté for 3-4 minutes until translucent.
Add the minced garlic and sliced mushrooms to the skillet. Cook for another 5 minutes until mushrooms are tender.
In a large mixing bowl, combine the dairy-free cream of mushroom soup, vegetable broth, black pepper, and dried thyme. Stir well.
Add the cooked noodles, sautéed vegetables, drained peas, and tuna to the bowl. Mix gently until all ingredients are evenly combined.
Transfer the mixture to a greased 9×13 inch baking dish. Sprinkle the shredded dairy-free cheddar cheese evenly over the top.
Sprinkle the crushed potato chips over the cheese layer to create a crunchy topping.
Bake uncovered in the preheated oven for 25-30 minutes, until the casserole is bubbly and the topping is golden brown.
Remove from oven and let cool for 5 minutes before serving.