Keep the diced butter and ice water in the refrigerator until ready to use.
Using a stand mixer bowl, add the flour and salt. Mix using the paddle attachment at the lowest speed (stir) for about 10-seconds.
Add chilled diced butter to the bowl. At the lowest speed, turn the mixer on and off quickly for a few seconds to coat the butter with the flour. This helps to prevent the flour from spilling over. Continue to mix on low speed (setting 2) until the flour and butter resemble wet sand with coarse crumbles and some pea-sized pieces remaining, about 75-seconds. Use fingers to break up any large pieces. Do not overmix. The dough should not bind together before adding the water. Alternatively, use a dough/pastry blender or your fingers to break the butter into the dough.
Gradually add 1 tablespoon of ice-cold water to the bowl. After each addition, turn the mixer on for 1 to 2-seconds. Only add enough water until the dough looks lumpy and hydrated but not wet or sticky. Where it just begins to clump together with small crumbles on the bottom of the bowl. All of the water may not be needed, about 5 to 6 tablespoons is typical. When the dough is pinched together, it should compress and hold, not be dry or crumbly. Do not over-mix. The dough will be pressed together before resting.
Press the dough into a 1” thick round disc, wrap it in plastic wrap, and place it in a resealable bag. Store in the refrigerator to rest for at least 4-hours, overnight, or up to 2 days.
Once removed from the refrigerator, allow the crust to sit at room temperature for about 5 to 10 minutes. This will make it easier to roll. If it’s still too hard, let it sit at room temperature until more pliable.
Dust the counter and top of the dough with flour. When rolling out, make sure to rotate and dust with flour underneath and on the top. This will prevent sticking and make it easier to transfer to the pie dish. Roll the dough into about a 14-inch circle, slightly thicker than ⅛-inch thick.
Place the rolled-out dough into a 9-inch pie dish and gently press against the sides and bottom. With a paring knife, trim the excess dough with a ½-inch overhang over the pie dish's edge. Tuck the extra underneath the bottom crust edges. Crimp by pinching the dough using the pointer and thumb fingers. Place the crust in the freezer for 20 minutes.
Set the oven rack in the middle position. Preheat the oven to 375°F (190°C).
To par-bake, place the chilled pie dish on a sheet pan. Place parchment paper on top of the crust and add the pie weights to cover just the bottom and sides, do not overfill. Bake until the edges are lightly golden and just begin to set, about for 20 minutes. Remove from the oven, and allow the weights to sit in the crust for about 4 to 5 minutes to press down any puffed areas. Remove the paper and weights, it will not be used again. Bake for another 5 minutes to dry the crust's bottom before filling. The crust may be a bit puffy, but it will deflate as it sits. Set on a wire rack while making the filling.
Filling
Evenly sprinkle half of the cheddar cheese and green onions into the par-baked pie crust. Top with all of the ham, followed by the remaining green onion, then cheese.
In a medium bowl, whisk together the eggs, egg yolk, whole milk, heavy cream, salt, pepper, and nutmeg. Slowly pour the egg mixture into the pie crust, allowing it to settle around the ingredients.
Bake the quiche on top of a sheet pan in the middle of the oven until the surface and crust are golden brown, about 45 to 50 minutes. The center will be slightly jiggly, and the temperature should be about 185 to 190ºF (85 to 88ºC) in the center. When a knife is inserted about 1-inch from the edge, it should come out clean and not wet.
Cool on a wire rack until it reaches room temperature, about 1 ½ to 2 hours. Slice or cool completely, cover, and refrigerate to serve the next day.
Notes
Using store-bought crust: For an unbaked refrigerated crust, follow the same instructions for shaping and par-baking in the recipe. If using a frozen crust, allow it to defrost before using.
Storing: Cool completely, cover, and refrigerate for up to 7 days.
Freezing: A whole quiche or slices can be wrapped and stored in a plastic bag for up to 1 month.
Reheating: Reheat refrigerated individual slices in the microwave in 15 seconds intervals on high power until warmed through. Alternatively, bake slices in the oven at 375ºF (191ºC) on a foil or parchment paper-lined sheet pan, about 10 to 15 minutes. If frozen, bake sliced for 20 to 25 minutes. Defrost a whole quiche, then bake until warmed through.