Preheat the oven to 375°F. Prick the bottom of a frozen pie shell using a fork. Bake for 5 minutes. Set aside.
In a small skillet, melt the butter. Cook the sliced green onion, green pepper, and red pepper until softened, about 2-3 minutes.
Layer ½ of the ham and ½ of the shredded cheese on the bottom of the par-baked pie shell.
Whisk together the heavy cream, eggs, and seasonings until fully combined. Add the cooked vegetables to the custard.
Pour ½ over the first layer of ham and cheese, then repeat with ham, cheese, and custard.
Place onto a baking sheet and bake for 10 minutes.
Lower the oven temperature to 350°F and continue to cook for an additional 30-40 minutes.
Rest on a cooling rack for at least 30 minutes before serving.
