Sprinkle the ham chunks and half of the cheese into the unbaked pie crust. Add the chopped peppers and red onion.
In a large mixing bowl, combine the eggs, milk, salt and pepper to taste, and tapioca flour. Use hand-held beaters to beat the mixture until it is thoroughly combined. You can also use a whisk to combine the ingredients.
Pour the egg mixture into the pie crust. Sprinkle the remaining cheese over the top of the egg mixture.
Bake for 35-40 minutes. The center may appear a little jiggly due to the melted cheese. Allow the quiche to set up for 5-15 minutes before cutting and serving.
Store leftovers in an airtight container in the fridge.