Preheat the oven to 375°F (190°C). Set the unbaked pie shell on a baking tray to ensure stable handling.
Warm the butter or oil in a skillet over medium heat. Add the diced onions along with both bell peppers. Sauté for approximately 4 to 5 minutes, stirring occasionally, until vegetables are tender. Incorporate the ham pieces and cook for an additional 1 to 2 minutes. Remove from heat and allow to cool slightly.
Evenly distribute the ham and vegetable mixture into the prepared pie crust. Scatter the shredded cheddar cheese over the top of the filling.
In a separate bowl, whisk together the eggs, milk or half-and-half, garlic powder, salt, and pepper until well blended. Gently pour this custard mixture over the filled crust, ensuring even coverage.
Transfer the quiche to the oven and bake for 35 to 40 minutes. The center should be firm, and the surface lightly golden. A knife inserted into the middle should come out clean when done.
Allow the quiche to rest for 5 to 10 minutes before slicing. If desired, finish with a sprinkle of chopped parsley or green onions just before serving.