Preheat your oven to 200°C (390°F). Roll out your pie crust on a lightly floured surface and fit it into your tart pan. Blind bake for 15 minutes until the crust is lightly golden, then set aside to cool slightly.
While the crust bakes, trim the woody ends from the asparagus. Cut the spears into 4-5cm (1.5-inch) pieces. Blanch the asparagus in boiling water for about 2 minutes until tender-crisp, then transfer to an ice bath to stop the cooking and preserve color. Drain thoroughly.
In a skillet over medium heat, add a drizzle of olive oil. Sauté the asparagus for 3-4 minutes until they are just tender and fragrant. Remove from heat and set aside.
In the same skillet, add a little more oil if needed, then toss in the spinach. Cook until wilted, about 2 minutes. Squeeze out as much excess moisture as possible, then chop roughly and set aside.
In a mixing bowl, whisk together the eggs and heavy cream until the mixture is smooth and slightly frothy. Stir in the grated Gruyère, nutmeg, herbs, salt, and pepper. This creates a rich custard base.
Spread the sautéed asparagus evenly over the partially baked crust. Add the wilted spinach on top, distributing it evenly. Pour the custard mixture carefully over the vegetables, filling the crust.
Bake the quiche in the oven at 180°C (355°F) for 30-35 minutes. The filling should be just set with a slight jiggle in the center and the top golden brown. Cover the edges with foil if they brown too quickly.
Once baked, remove the quiche from the oven and let it rest on a cooling rack for about 10 minutes. This helps the custard set further and makes slicing neater.
Slice the quiche into wedges with a sharp knife, revealing the vibrant green vegetables and creamy custard. Serve warm or at room temperature, enjoying the flaky crust and flavorful filling.