1 refrigerated pie crust, or homemade pie crust for a single-crust pie
2 tsp olive oil
1 small onion, diced
10 thin asparagus spears, ends trimmed, cut into 1/4-inch pieces
2-3 large button mushrooms, diced
3 links hot Italian turkey sausage, removed from the casing
1/4 tsp fennel seeds
1/2 tsp dried thyme leaf or 1 tsp fresh thyme leaves or flat-leaf parsley
4 eggs + 1 egg
2 Tbsp Greek yogurt
1/4 cup grated Gruyere cheese
1/2 tsp kosher salt
1/2 tsp fresh black pepper
Unroll one pie crust (for a 9-inch pie) and center it in a pie plate. Crimp the edges by hand, or press a design all around with a fork. Set aside.
In a nonstick frying pan, heat the olive oil over low-medium heat. Add the onion, asparagus, mushrooms and sausage and cook, stirring occasionally, for 10 minutes until the sausage is lightly browned and the onions are translucent. Add the fennel seeds and thyme, stir to combine, and set aside to cool for at least 15 minutes. (This step is important; if the filling is too hot, it will melt the pastry before the quiche gets to the oven. The filling also can be made in advance and refrigerated.)
In a large measuring cup or bowl, whisk 4 eggs until they are smooth. Add the yogurt, and whisk again. Stir in the cheese, salt and pepper.
Scatter the vegetable and sausage filling evenly in the pie crust. Pour the egg mixture over the top. Push it around with a rubber spatula so it covers all of the vegetables.
In a small bowl, beat 1 egg with 1 teaspoon of water. Using a brush, paint the crust with the beaten egg.
Bake for 40 minutes. Let sit at room temperature for 10 minutes before serving. Serve warm, at room temperature, or cold.