Par-bake the crust. Preheat the oven to 425°F. Prepare the pie crust in a pie plate and prick the bottom and sides with a fork. Brush the Dijon mustard over the bottom of the crust. Bake directly on the center oven rack for 8–10 minutes, until just beginning to brown. Remove from the oven and reduce the temperature to 350°F.
1 unbaked pie crust, 2 Tbsps Dijon mustard
Drain the zucchini. While the crust bakes, place the grated zucchini in a colander and toss with ½ teaspoon salt. Let drain for at least 5 minutes while you prepare the filling.
1 cup grated zucchini squash, ½ tsp salt
Make the filling. Beat the softened cream cheese until smooth. Add the heavy cream, egg yolks, and whole egg, mixing well after each addition. Add ½ teaspoon salt and the black pepper and beat until smooth.
8 ounces cream cheese, 2 large egg yolks, 1 large egg, ½ tsp salt, ½ tsp fresh cracked black pepper, ½ cup heavy whipping cream
Squeeze the zucchini. Using your hands or a clean kitchen towel, squeeze the grated zucchini well to remove as much excess moisture as possible.
Assemble the quiche. Place the par-baked crust on a baking sheet. Sprinkle 1 cup Monterey Jack over the bottom, followed by the corn and drained zucchini. Pour the cream cheese mixture evenly over the vegetables. Top with the remaining 1 cup cheese, a little freshly ground black pepper, and the reserved zucchini slices, if using.
2 cups Monterey Jack cheese, ½ cup corn
Bake the quiche. Bake at 350°F for about 45 minutes, until the filling is set in the center and the top is lightly golden. If the crust or top begins to brown too quickly, loosely cover with foil.
Cool and serve. Let the quiche rest for about 5–10 minutes before slicing. Serve warm or at room temperature, or cool completely and refrigerate to serve later.