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Step 1
Preheat the oven to 350°F. Par-bake a frozen pie shell lined with a bag of beans (or line with tin foil and use beans or pie weights) for 40 minutes as directed in my all-butter pie crust recipe.
Step 2
Once the pie shell has pre-baked, remove it from the oven, set the beans or aluminum foil aside, and raise the oven temperature to 375°F.
Step 3
Melt the butter in a large skillet over medium heat, add the ham and onion and cook until the onion is softened. While the onions cook, bring a small saucepan of water to a boil. Add the broccoli and blanch for 1 minute then drain the broccoli, roughly chop it, and set aside.
Step 4
Scatter the cheese on the pre-baked pie shell then layer the ham and onion, and then the broccoli.
Step 5
Whisk the half-and-half with the eggs and white pepper in a bowl or a 4-cup measuring cup. Pour the custard over the layered ingredients, filling the pie shell to the brim but not overflowing. Depending on how deep your pie tin is, you may have extra custard you can discard.
Step 6
Bake the quiche for 30-35 minutes or until the top puffs and begins to brown and a cake tester or toothpick comes out clean while the center may still be somewhat jiggly.
Step 7
Remove from the oven and transfer to a cooling rack where the egg will continue to set. Cut into slices and serve warm or at room temperature. If making ahead, bring to room temperature for 15-30 minutes before serving.