Preheat the oven to 375°F and grease a 9x13 baking dish. Cook the spaghetti in salted water for 2 minutes less than the package directions, then drain.
Melt the dairy free butter in a large skillet over medium heat. Cook the mushrooms for 6 minutes until browned, add the onion for 4 minutes, then stir in the garlic for 30 seconds.
Sprinkle in the flour and stir for 1 minute. Pour in the white wine and let it bubble for 1 minute.
Slowly whisk in the chicken broth and oat milk and simmer for 4-5 minutes until thick and creamy. Stir in the nutritional yeast, thyme, nutmeg, salt, and pepper.
Toss the spaghetti, chicken, and peas with the sauce until evenly coated, then spread into the baking dish.
Mix the panko, nutritional yeast, and olive oil and sprinkle it over the top. Cover with foil and bake for 15 minutes, then uncover and bake 10-15 minutes more until golden and bubbling.
Rest for 5 minutes and sprinkle with parsley before serving.