In a large pot, heat the oil over med-high heat. Add the onion and saute until soft. Add the asparagus and continue sauteing until they turn bright green. Add the garlic and thyme, cook for 2 minutes and then add the stock.
Bring the mixture to a boil and then simmer over low heat for 10 minutes or until the asparagus is tender.
With an immersion blender, puree the mixture until all the asparagus is no longer in large pieces.
Stir in the Greek yogurt and puree for one minute.
Serve immediately. (Note: For the garnish, I sauteed some asparagus tips seperately and topped the soup before serving.)