Preheat the oven to 375°F (190°C).
Bring a pot of salted water to a boil. Add the cauliflower florets and cook for 5 minutes until tender but not mushy. Drain well and set aside.
Heat olive oil in a large skillet over medium heat. Add the chopped onion, minced garlic, and diced celery. Cook for 5 minutes until the vegetables are softened.
In a large mixing bowl, combine the cooked vegetables, mayonnaise, sour cream, Dijon mustard, salt, and black pepper. Mix well to create a creamy sauce.
Add the drained tuna to the bowl and gently fold it into the creamy mixture.
Add the cooked cauliflower to the bowl and stir to combine everything evenly.
Transfer the mixture into a greased 8×8 inch baking dish.
Sprinkle the shredded cheddar cheese, mozzarella cheese, and grated Parmesan cheese evenly over the top of the casserole.
Bake uncovered in the preheated oven for 20 minutes, or until the cheese is melted and bubbly and the casserole is heated through.
Remove from the oven and let it cool for 5 minutes. Sprinkle chopped fresh parsley on top before serving.