Preheat oven to 350 degrees F. Mist a 10-inch pie dish with nonstick cooking spray; set aside.
Cut woody ends off of the asparagus spears. Take half the spears and cut off the top 4-5 inches to use on the top, if desired. Cut remaining asparagus into 1-2 inch pieces. If your asparagus is thick, halve the asparagus to create 2 thinner stalks before cutting into smaller pieces. Sprinkle the smaller pieces into the bottom of the dish and reserve the 4-5 inch pieces.
In a medium bowl, whisk to combine the eggs, milk, salt, pepper, and thyme. Pour the egg mixture over the asparagus in the dish and sprinkle with the shredded cheese.
Top with the 4-5 inch asparagus spears in a star-burst arrangement.
Bake quiche for 60-75 minutes or until golden and eggs are set. Allow quiche to cool for 10-15 minutes before cutting.