Preheat your oven to 375°F (190°C). Place your pie crust in a 9-inch pie dish and crimp the edges. Prick the bottom with a fork several times to prevent bubbling.
Blind bake the crust. Line the crust with parchment paper and fill with pie weights or dried beans. Bake for 12 minutes, then remove weights and bake for another 5 minutes until lightly golden. Set aside to cool slightly.
Prepare the asparagus. Bring a pot of salted water to boil. Blanch the asparagus pieces for 2-3 minutes until bright green and slightly tender. Drain and immediately plunge into ice water to stop the cooking. Pat dry with paper towels.
Sauté the aromatics. Melt butter in a skillet over medium heat. Add the diced onion and cook for 3-4 minutes until softened. Add garlic and cook for another minute until fragrant. Remove from heat.
Make the custard mixture. In a large bowl, whisk together eggs, heavy cream, milk, salt, pepper, and nutmeg until well combined and slightly frothy.
Assemble the quiche. Spread the sautéed onion and garlic evenly over the bottom of the pre-baked crust. Layer the blanched asparagus on top. Sprinkle both cheeses evenly over the vegetables.
Pour and bake. Carefully pour the egg mixture over the filling, making sure it distributes evenly. The liquid should come just below the rim of the crust.
Bake until set. Place the quiche in the oven and bake for 35-40 minutes. The center should be just set with a slight jiggle, and the top should be golden brown.
Cool before serving. Let the asparagus quiche rest for at least 15 minutes before slicing. This allows the custard to firm up properly and makes cutting much easier.