Preheat your oven to 375°F (190°C).
Bring a large pot of salted water to a boil. Cook the pasta according to the package instructions until al dente. During the last minute of cooking, add the frozen peas. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and sauté for about 5 minutes until softened.
Add the minced garlic and cook for another minute until fragrant.
Add the sliced mushrooms to the skillet. Cook for about 8-10 minutes, stirring occasionally, until the mushrooms are browned and have released their moisture.
Sprinkle the flour over the mushrooms and stir well to coat. Cook for another 2 minutes to get rid of the raw flour taste.
Gradually add the vegetable broth, stirring constantly to prevent lumps. Then add the almond milk and bring the mixture to a simmer.
Stir in the nutritional yeast, dried thyme, dried oregano, salt, pepper, soy sauce (or tamari), and white wine (if using). Let the sauce simmer for about 5-7 minutes until it thickens.
Stir in the chopped parsley and adjust seasoning if needed.
Add the cooked pasta and peas to the skillet with the sauce. Toss everything together until the pasta is well coated with the sauce.
In a small bowl, mix the breadcrumbs with the garlic powder and olive oil until they are evenly coated. Add the vegan Parmesan if using.
Transfer the pasta mixture to a large baking dish. Spread it out evenly. Sprinkle the breadcrumb mixture evenly over the top.
Bake in the preheated oven for about 20-25 minutes, until the top is golden brown and crispy.
Let the tetrazzini cool for a few minutes before serving. Garnish with extra parsley if desired.