In a large stock pot, add olive oil and ½ inch pieces of asparagus tips. Cook for 5 minutes on medium heat with lid on until asparagus has started to soften. Then add chicken broth to the pot. Cook on high with lid on for 25 minutes. During the last 5 minutes add the asparagus tips and cook until just tender. Remove the tips and set to the side.

Once the asparagus is done, carefully pour the broth and asparagus into a blender. Blend until pureed (about 20-30 seconds). Return back to the stock pot. Add salt and pepper and heavy cream. Cook for 5 minutes on medium-high until cream has thickened and soup is hot. Serve immediately with freshly ground black pepper and steamed asparagus tips.