Preheat your oven to 375 degrees Fahrenheit. If using a store-bought crust, place it into a 9-inch pie dish and crimp the edges as desired.

In a medium skillet over medium heat, warm the olive oil. Add diced onion and sauté for 3 to 4 minutes until softened. Stir in the broccoli and cook for an additional 4 to 5 minutes until the florets turn bright green and tender. Remove from heat and allow to cool slightly.

In a large mixing bowl, whisk together the eggs, milk, salt, pepper, and nutmeg until well combined.

Sprinkle the shredded cheddar cheese evenly over the bottom of the prepared pie crust. Add the cooked broccoli and onion mixture over the cheese.

Pour the egg mixture over the filling, making sure it spreads evenly.

Place the quiche on a baking sheet for easier handling and bake for 40 to 45 minutes, or until the center is set and the top is golden. If the crust begins browning too quickly, tent the edges with aluminum foil.

Remove from the oven and let cool for at least 10 minutes before slicing. Serve warm or at room temperature.