Parboil cauliflower in water and salt for 4 minutes. Drain and let stand.
Sauté onion in 1 tbsp oil until glassy.
Then add ground beef, salt, pepper, and nutmeg. Cook on medium flame stirring occasionally till cooked, let stand.
Melt butter and oil over low flame. Remove from flame and stir in the flour, blending thoroughly. Return to flame, and as the mixture starts to bubble, move to side of flame and add 1/3 cup of milk very gradually, stirring constantly to prevent lumps. Return to low flame and cook, stirring and increasing the sauce in small doses with stock, the remaining milk, and seasoning until it reaches the desired thickness (should me creamy thick). Remove from stove and quickly add the egg.
Mix 1/4 of sauces with cauliflower then in a small greased baking dish arrange half of the cauliflower. Add a layer of the meat, then the second half of the cauliflower. Top with the remaining sauce and bake for 30 minutes or when top is golden at 350°F.