Trim the bottom ends off of the asparagus and discard them. Cut the asparagus tops off into 1-inch pieces.
Heat the olive oil in a skillet over medium heat. Add the chopped onion and cook, stirring occasionally, until it begins to soften, 2-3 minutes. Add the asparagus and cook for 2-3 minutes more. Remove the pan from the heat.
In a medium bowl, whisk together the eggs, whole milk, salt and pepper.
Place asparagus and onion in the bottom of the frozen pie crust. Crumble the goat cheese over the top of the vegetables. Pour the custard over the filling.
Bake quiche for 35-45 minutes, until the eggs are set in the center. Check on quiche starting at 25 minutes and tent with foil if crust is browning too quickly.