Preheat oven to 350°F. (regular bake setting/not fan assisted)
Using the largest holes on a box grater, shred potatoes. Place in a large bowl and toss with 1 tsp. salt and 1/2 tsp. pepper. Transfer potatoes to a clean dish towel, gather together the ends of the towel and thoroughly wring out excess liquid over the sink. Transfer potatoes to a bowl and set aside.
Heat oil and 2 Tbsp. butter in a 10" (top diameter) cast-iron skillet over medium-high until butter is melted. Add potatoes and immediately start forming into a crust by pushing potatoes flat against the bottom and sides of the pan with a 1/2-cup dry measuring cup. Continue cooking, pressing potatoes up sides of the pan if they start shrinking until potatoes are bound together and the bottom of the crust is starting to brown about 10 minutes. Remove pan from heat and set aside.
Meanwhile, melt 1 Tbsp. butter in a small skillet over medium heat. Add shallots and sauté until translucent, about 5 minutes. Set aside.
In a large bowl, whisk eggs, half-and-half, salt, pepper, mustard powder and nutmeg. Set aside.
Sprinkle cheese and sautéed shallots evenly over bottom of the potato crust, then pour in egg mixture. Arrange asparagus (and chives, if using) decoratively on top.
Bake until quiche is set and crust is well browned, 30-35 minutes. Let cool at least 10-15 minutes, or to room temperature before cutting into wedges and serving from the pan.
Notes
You can experiment with different cheeses or a combination of cheeses.Be sure to use all your muscles to wring out the moisture from the potatoes. The drier they are to start with, the better the result. Also, you don't want to skimp on the time needed to brown/set the crust on the stove top before placing it in the oven, as it's the key to a lovely crisp potato crust.Do let the quiche sit a bit to set up before serving. It's at its best served slightly cooled, rather than straight from the oven (in my opinion :)Be sure to read the notes above this Recipe Card, for more tips on making this recipe.