Preheat oven to 325 degrees F (165 degrees C). Unroll pie crust and press into an 8-inch pie dish.
Heat olive oil in a skillet over medium heat; cook and stir green onions until wilted and beginning to brown, 2 to 3 minutes. Remove from heat. Spread ham over prepared pie crust and top with green onions.
Whisk egg substitute, evaporated milk, and mozzarella cheese in a bowl. Pour over ham mixture. Sprinkle with Parmesan cheese and garnish with chives.
Bake in preheated oven for 20 minutes. Increase heat to 350 degrees F (175 degrees C) and continue baking until quiche is browned, 15 to 20 minutes. Remove from oven and allow quiche to rest until eggs are set, about 30 minutes more.
