Preheat oven to 400 degrees F (200 degrees C).

Cook bacon in a large skillet over medium heat until evenly brown and crisp. Drain on paper towels, crumble and set aside.

Heat oil in a large skillet over medium-high heat. Add onions; cook and stir until translucent. Reduce the heat to medium and add the portobello mushrooms. Continue cooking until the mushrooms are tender. Set aside.

Bring a saucepan of salted water to a boil over high heat. Cook asparagus in boiling water until just tender, 1 to 2 minutes. Immediately drain and run under cold water to cool.

Brush the pie shell with the beaten egg white, if using. Place the onion and mushroom mixture, asparagus, and bacon into the bottom of the pie shell. Sprinkle the Cheddar and feta cheeses over the vegetables. In a small bowl, whisk together the eggs, cream, salt, and pepper until smooth. Pour this mixture over the vegetable and cheese filling.

Bake uncovered for 35 to 40 minutes, or until firm and lightly browned on top. Let cool to room temperature before serving.