In a large pot bring water to a boil and add the pasta. Cook according to package directions. Drain and set aside.
While the pasta cooks, heat the oil in a large skillet over medium-high heat. Add the chicken and season with a bit of salt, black pepper, thyme, garlic powder and oregano. Cook for 5 minutes, stirring occasionally until browned and cooked through. Add 1 tbsp minced garlic and cook for another minute, until fragrant. Transfer to plate and set aside. Do not overcook.
Add vegan butter to the same skillet and melt over medium-high heat. Add remaining minced garlic and asparagus and sauté for 1 minute, until just starting to turn bright green. Whisk in the coconut milk, lemon juice, lemon zest, garlic powder, oregano, thyme, nutmeg, parmesan (or nutritional yeast), and mozzarella cheese.
Allow the sauce to thicken and cheese to melt. Add the drained pasta and chicken back into the skillet. Season with salt and black pepper to taste (I used about 1½ teaspoons salt and ½ teaspoon black pepper). Toss to coat well until everything is heated through.
Serve hot and sprinkle with nutritional yeast or more parmesan cheese, chopped parsley, and lemon slices, if desired.