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

Brush pie shell with beaten egg white. Place onion-mushroom mixture, asparagus, and crumbled bacon into the bottom of pie shell. Sprinkle with Cheddar and feta cheese.

Whisk together eggs, cream, salt, and pepper in a medium bowl until smooth. Pour over vegetable-cheese filling in pie shell.

Bake uncovered in the preheated oven until filling is firm and the top is lightly browned, 35 to 40 minutes. Let cool to room temperature before serving.