Add the butter to a skillet over medium-high heat.
When the butter is melted, add the onion and sauté until it's translucent, about 4 to 5 minutes.
Add the ham and cook for another 3 to 4 minutes.
Add the arugula and toss until it's just wilted, about a minute.
Remove the pan from the heat so it can slightly cool.
Add the eggs, half-and-half, half the green onions, salt, and pepper to a large bowl and whisk until frothy.
Add the cheese and stir to combine.
Liberally spray a 12-cup muffin tin with nonstick cooking spray.
Divide the arugula mixture between all 12 cups, about a tablespoon each.
Next divide the egg mixture between all 12 cups, about an eighth of a cup each.
Bake for 10 minutes, and then rotate the pan.
Bake for another 10 minutes or until the center is set and the top is lightly browned.
Remove the pan from the oven, and allow the quiches to cool 5 to 10 minutes.
Use a small spatula to scoop them out.
Serve with the remaining green onions sprinkled on top, if desired.