Set the oven temperature to 375°F.
Add the cheese to the base of the quiche. Then add the squash and leeks. The vegetables should be level with the top of the crust. Save any extra filling to make mini quiches in buttered ramekins.
½ cup (2 ounces) shredded gruyere or Swiss cheese
Whisk together the half-and-half, eggs, thyme, mustard, remaining salt, and pepper in a small bowl or a large measuring cup.
1½ cups (12 ounces) half-and-half, 3 large eggs, 2 teaspoons fresh thyme, 1 teaspoon Dijon mustard, ¼ teaspoon black pepper
Transfer the vegetable-filled crust to your oven, and quickly but carefully pour the egg mixture on top of the squash and leeks until it comes very nearly to the top of the crust.
Bake for 35 to 40 minutes until the custard is no longer liquidy, but there is still a bit of jiggle.
Serve warm or at room temperature.