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 sautéing. Use a separate cooking pan; the stoneware dish goes only in the oven.

Steam the fresh broccoli until just barely cooked and brighter green, with florets still holding their shape. Set aside uncovered and let surface water drain away; the florets 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 salt and black pepper, and cook until beginning to brown. Add the sliced mushrooms and sauté until softened and cooked, then remove from the heat.

Distribute the steamed broccoli, cooked onion and mushrooms, and cooked shredded chicken across the greased dish. Break apart compact chicken clumps and keep an even filling depth through the corners.

Whisk the measured homemade chicken meat stock, completed rich homemade coconut milk, eggs, optional nutmeg, and a generous pinch of salt and pepper until evenly creamy with no strands of unmixed egg. Pour across the filling and gently settle to distribute. Do not add extra stock to submerge the broccoli tops.

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

Rest 5–10 minutes on a heat-safe support before spooning 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.