Place bacon in a large, deep skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon on a paper towel-lined plate. Crumble bacon when cool; set aside. Reserve 1 tablespoon bacon drippings in a small bowl.

Melt butter with bacon drippings in a large saucepan over medium heat.

Cook and stir celery and onion in hot butter-drippings until onion is translucent, about 4 minutes. Whisk in flour and cook for 1 minute. Whisk in chicken broth and bring to a boil. Add potato and asparagus, reserving asparagus tips for later. Season with salt and ground black pepper. Reduce heat and simmer soup for 20 minutes.

Pour soup into a blender, filling the pitcher no more than halfway. Hold down the lid of the blender with a folded kitchen towel and blend in batches until smooth. Alternatively, you can use a stick blender to purée soup directly in the pot.

Cook and stir mushrooms and asparagus tips in the skillet used for bacon until mushrooms release their liquid, 5 to 8 minutes. Season with salt and ground black pepper, if needed.

Stir mushrooms, asparagus tips, and half-and-half cream into the puréed soup. Cook until thoroughly heated.