Place asparagus ends and Parmigiano-Reggiano rinds into a pot. Cover with at least 1 inch of water. Bring to a boil.
Reduce to a simmer. Cook until the asparagus can be mashed with a potato masher about 45 minutes to 1 hour.
Strain out the ends and rinds through a mesh strainer.
Add the potatoes. Bring back to a boil. Then simmer until the potatoes are soft, about 15 to 20 minutes.
If adding spinach add now and stir until wilted.
Blend with an immersion blender until completely smooth or leave some chunks.
Season with salt and pepper.