Cook pasta according to the instructions on the package. Drain and keep warm.
In a large skillet, heat up oil over a medium heat.
Add asparagus and saute until soft, about 2 to 3 minutes.
Add garlic and stir it in. Cook for 30 seconds.
In a medium mixing bowl, whisk together milk and cornstarch.
Add the milk mixture to the sauteed asparagus, gradually, ¼ of a cup at a time, stirring constantly. Let the sauce thicken before adding more milk. Repeat until you use all the milk.