Preheat oven to 375°F (190°C). Place the pie crust into a 9-inch pie dish.
Melt butter in a skillet over medium heat. Add onions and cook until softened. Stir in spinach and cook briefly until wilted. Remove from heat.
Spread spinach, onions, and diced ham evenly over the pie crust. Sprinkle with shredded cheese.
In a medium bowl, whisk together eggs, milk, salt, pepper, and nutmeg until smooth.
Pour the egg mixture evenly over the filling in the crust.
Bake for 40–45 minutes, or until the quiche is set in the center and the crust is golden brown.
Remove from oven and let cool for 10 minutes before slicing.
Garnish with chopped green onions and serve warm.