Preheat oven to 400 degrees.
Butter and flour (or spray with non-stick baking spray) a 9″ tart pan with a removable bottom. Lay out the pie dough in the pan, pressing down and into the sides. Trim off any excess dough from the edges.
Prick the dough with the tines of a fork and then brush the bottom and sides with egg white.
Place the tart on a baking sheet and bake for 10 minutes, until the egg white is set. Set aside to cool for at least 10 minutes.
Meanwhile, cook the pancetta in a skillet over medium-high heat until crispy. Drain on a paper towel and set aside.
While the pancetta is cooking, place the asparagus tips in a microwave safe dish and cover with water. Microwave on high for 2 to 3 minutes until the asparagus is crisp tender. (Or, blanch in boiling water for 1 minute on the stove). Drain asparagus and set aside.
In a medium bowl, whisk together the eggs and mascarpone until well combined. Stir in the green onion, pancetta and shredded gryuyère.
Pour the egg mixture into the tart shell. Decorate the top with the blanched asparagus spears.
Bake for approximately 20 minutes until the top is browned and the center is set.
Cool tart for at least 5 minutes, then remove from the pan. Serve warm, or at room temperature.
If made ahead, tart can be reheated in a 350 degree oven for 15 minutes on a baking sheet.