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. Set aside the skillet.

Melt butter with 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. Holding down the lid of the blender with a folded kitchen towel, start the blender, using a few quick pulses to get soup moving before leaving it on to purée. Purée in batches until smooth and pour into a clean pot. Alternately, you can use a stick blender and purée soup right in the cooking pot.

Cook and stir mushrooms and asparagus tips in the same 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 puréed soup. Cook until thoroughly heated.

Portion soup into bowls and garnish with crumbled bacon.