Preheat your oven to 180°C (350°F) and lightly grease your ovenproof dish or pie plate with butter or non-stick spray.
In a large mixing bowl, whisk together the eggs until they are well combined and slightly frothy, about 30 seconds.
Add the milk or cream to the eggs and whisk again until smooth. Stir in salt, pepper, and a pinch of nutmeg if using.
In a sauté pan, heat a teaspoon of olive oil and cook the spinach or zucchini until just tender and fragrant, about 3-4 minutes. Set aside to cool slightly.
Layer the sautéed vegetables and chopped ham evenly in the prepared dish. Sprinkle the shredded cheese over the top, distributing it evenly.
Pour the egg mixture over the layered fillings, ensuring everything is covered evenly. Gently tap the dish to settle the ingredients and release any trapped air bubbles.
Place the dish in the oven and bake for 35-40 minutes, until the top is golden and slightly puffed, and the edges are pulling away from the dish.
Check for doneness by inserting a knife into the center—if it comes out clean and the top is golden, your quiche is ready.
Remove the quiche from the oven and let it rest for 5-10 minutes. This helps it set and makes slicing easier.
Slice into wedges and serve warm or at room temperature. Garnish with fresh herbs if desired, and enjoy the comforting, savory flavors.