Preheat oven to 350 degrees F (176 C). Roll out the dough and place in a 9-inch pie plate, or if using a ready-made crust, defrost according to package directions.
Remove the woody ends from the asparagus. Slice the asparagus into small ¼-inch pieces.
Heat the olive oil in a large skillet over medium-high heat. Once hot, add the minced garlic and sliced asparagus and cook for 3 minutes, stirring occasionally. Add the spinach and cook just till the spinach has wilted.
Spread the spinach-asparagus mixture across the base of the pie dough in an even layer.
Crack the eggs into a mixing bowl. Whisk till the yolks break. Add in the milk, half the cheese, and the salt. Whisk till combined.
Pour the egg mixture on top of the spinach mixture. Spread the remaining cheese across the eggs.
Bake for 45 to 50 minutes or until the center of the quiche has set. Allow the quiche to cool for 5 minutes before slicing and serving.