Preheat oven to 350˚ F. Butter a 9-inch X 11-inch baking dish.
Set aside 3 or 4 of the asparagus spears. They will be arranged on the top of the egg bake just before baking. Slice the remaining spears into 1-inch lengths. Prep the scallions, leek, and onion. Warm the olive oil in a large skillet over medium heat. Add the asparagus, scallions, sliced leek and diced onion to the skillet and sauté for 2 - 3 minutes.Grate the potato using a large holes on a box grater and add to the skillet, along with the garlic, salt and Herb de Provence. Sauté for 10 minutes, or until softened. Transfer the veggies to the prepped baking dish to cool slightly.
Add the asparagus spear and artichoke hearts to the same pan to sear for a couple of minutes. Set aside.
Separate the yolks from the whites of 4 of the eggs. Reserve the egg whites in a medium bowl. Place the separated yolks in a large bowl along with the remaining eggs, and whisk together. I use a stick blender with a whisk attachment to whisk this many eggs, as it's very quick. Stir in the milk and cheeses. Using a hand mixer, whip the 4 egg whites to a medium-firm peak, and fold into the egg mixture using a rubber spatula.
Pro tip: It's best to fold the whipped egg whites into the egg and cheese in thirds for best results. Don't try to fold them in all at once.
Pour the eggs over the sautéed veggies in the baking dish. Top with the seared artichokes and asparagus spears.
Arrange the baking dish on a baking sheet and bake on the middle rack for 75 minutes, or until firm in the middle. The eggs will begin to brown after the first half hour, and I recommend covering the dish with foil at this point for the remaining baking time.
Sprinkle 1 tablespoon grated Parmesan cheese over the top of the cooked egg bake, and allow to sit for 10 minutes before serving.