Preheat your oven to 400°F. While it heats, trim the tough ends from the asparagus and cut into 1-inch pieces, then slice the leek (white and light-green parts only) into 1/4-inch rounds. Dice the ham into 1/2-inch pieces and shred the Gruyere cheese. Having everything prepped and ready will make the assembly process smooth and efficient.
Place the refrigerated pie crust in a 9-inch pie pan and prick the bottom with a fork. Line with parchment paper and fill with pie weights or dried beans to prevent puffing. Bake for 10 minutes until the crust is set but still pale. Remove the weights and parchment, then brush the warm crust lightly with Dijon mustard—this adds subtle flavor and helps seal the crust to prevent sogginess.
Heat the olive oil in a large skillet over medium heat. Add the sliced leeks and sauté for 2-3 minutes until they begin to soften, then add the asparagus pieces and cook for another 2 minutes until just tender-crisp. Don't overcook—the vegetables will continue to cook in the oven. I like to taste a piece of asparagus to make sure it has a slight bite to it, which keeps the quiche from becoming mushy.
In a medium bowl, whisk together the eggs, milk, and heavy cream until well combined. Season with kosher salt, black pepper, and ground nutmeg. Whisk gently but thoroughly to ensure the eggs are fully incorporated and the custard is smooth. Room-temperature milk helps the custard cook evenly throughout the quiche.
Spread the sautéed leeks and asparagus from Step 3 evenly over the pre-baked crust, then scatter the diced ham over the vegetables. Pour the custard mixture from Step 4 over everything, allowing it to settle around the filling ingredients. Sprinkle the shredded Gruyere cheese evenly over the top. Bake at 400°F for 40 minutes until the custard is set but still slightly jiggly in the very center—it will continue to set as it cools. The top should be golden brown.
Remove the quiche from the oven and let it rest on a cooling rack for 15 minutes before slicing. This resting period allows the custard to set completely and makes the quiche easier to cut into clean slices. Slice into wedges and serve warm or at room temperature.