Blanch asparagus and cauliflower pieces in water water until tender crisp.
In a large nonstick skillet, heat the oil. Sauté the onion until golden, about 7 minutes. Add the garlic and cook, stirring, 1 minute longer. Stir in the asparagus, cauliflower, eggs, parsley, salt, pepper, thyme and nutmeg.
Reduce heat and cook covered until set and browned on bottom, about 10 to 15 minutes. Loosen the edges with a knife and invert onto a warm platter or serve directly from skillet.