Preheat oven to 350°F. Butter a deep casserole dish.
In a saucepan, whisk the arrowroot powder with milk. Gently heat until it begins to thicken, whisking frequently. Whisk in the salt and dash of paprika.
Sautée the shallot, celery, and garlic in 2 T butter or coconut oil until tender. Add mushrooms and sautée until the liquid has evaporated.
Stir the drained tuna, peas, sautéed vegetables, and pasta into the milk. Pour into the baking dish and top with the grated cheese.
Bake 25-30 minutes in the preheated oven, or until the cheese is melted and lightly browned on top.