Preheat the oven to 350°F. Grease an oven-safe broad four-quart rectangular baking dish with half the measured coconut oil. Reserve the other half for the onion and mushrooms. Keep stoneware off the stovetop.

Steam the broccoli until just barely cooked and brighter green, with florets still holding together. Set aside uncovered and let surface water drain away; the broccoli will finish cooking in the oven.

Melt the remaining half of the coconut oil in a stainless-steel or enameled pan. Add the diced onion, season with sea salt and black pepper, and cook until beginning to brown. Add the sliced mushrooms and sauté until softened and cooked, then take the pan off the heat.

Distribute the broccoli, cooked onion and mushrooms, and shredded cooked chicken evenly in the greased dish. Break up compact clumps of chicken and spread the filling into the corners without one tall central mound.

Whisk the measured homemade chicken meat stock, completed cultured cream, eggs, optional nutmeg, and a generous pinch of salt and pepper until evenly creamy with no separate cream blobs or egg streaks. Pour across the filling and gently settle it to distribute the liquid. Do not add extra stock to submerge the broccoli.

Bake 35–40 minutes until the middle is hot through and the egg mixture is set around the filling, without a loose pool of unmixed liquid in the center. Check the center as well as the edges.

Rest 5–10 minutes before serving, then spoon chicken, vegetables, and the creamy mixture into portions. Refrigerate leftovers covered. Reheat covered until the center is heated through; a small splash of the same stock can loosen a thickened portion if needed.