Heat the avocado oil in a large, deep pot over medium heat until the oil begins to shimmer.
Add the diced white onion and minced garlic. Sauté for 3–4 minutes, stirring as needed, until the onion becomes lightly translucent.
Stir in the chopped broccoli and continue cooking for another 3–4 minutes, or until the florets turn vivid green and soften slightly. Season the vegetables with the salt and ground black pepper.
Add the drained tuna to the pot. Using a wooden spoon, gently break the tuna into smaller pieces while thoroughly combining it with the broccoli and aromatics.
Pour in the chicken broth and full-fat coconut milk. Stir until the ingredients are evenly distributed, then raise the heat to medium-high and bring the liquid to a gentle boil.
Add the gluten-free shell noodles once the mixture begins boiling. Reduce to a steady simmer and cook for approximately 10–12 minutes, stirring frequently, until the pasta reaches the desired tenderness.
During the final minute of cooking, stir continuously to encourage the liquid to reduce and develop a thicker, creamier consistency. For softer noodles, continue simmering for an additional 1–2 minutes.
Stir in 1–2 tablespoons of nutritional yeast, using the amount that best suits your preferred level of savory, cheese-like flavor.
Serve the casserole while hot and finish each portion with freshly chopped parsley.