Break off the tough ends of each asparagus stalk. Cut off the tips and cut the stalks into ½ to ¾ inch slices.
Bring a small sauté pan with ½ inch of water and ½ teaspoon salt to a boil. Once boiling, add the asparagus and blanch for 2 minutes. Drain immediately and submerge asparagus pieces in a bowl of ice water. Once cooled, separate the tops (to be used onto top of the quiche) from the stalk pieces, dry and set the side.
In a small sauté pan, heat 1 teaspoon canola oil. Once the pan and oil are hot, saute shallots for 1 ½ minutes. Remove from pan and set to the side to cool.
In a large mixing bowl, whisk eggs, heavy cream, Dijon, ½ teaspoon, ¼ teaspoon pepper, dill and parsley. Add the shredded Jarlsberg, grated Grana Padano and asparagus pieces (do not include asparagus tops). Stir to incorporate into the egg mixture.
Preheat oven to 350 degrees. Peel and shred the potatoes. Toss with 1 teaspoon salt and ½ teaspoon pepper. Place shredded potatoes in a dish cloth and wring out excess water from the potatoes. Short Cut: Purchase refrigerated hashbrowns.
Heat 2 tablespoons of butter in a 10-inch cast iron skillet over medium heat until the butter is melted. Add the potatoes, pushing them down to the bottom and sides of the pan. Cook them for 10 minutes (pushing them up the sides if they start to shrink) or until they start to form a brown crust. Remove from heat.
Pour quiche mixture into the hashbrown crust. Top with asparagus tops.
Bake for 35-40 minutes or until quiche is set and crust is well browned (175-degree internal temperature). Let it rest for 5-10 minutes before cutting. Quiche can be served at room temperature.
Reheat: The quiche can be made a day in advance. Refrigerate, covered with plastic wrap. Bring the pan out for 30 minutes prior. Reheat at 325 degrees for 20-25 minutes (or until it reaches 165 degrees internal temperature).