In a medium pot, heat olive oil.
Add onions to and sauté until translucent, 3-4 minutes. Add garlic and roasted poblano peppers.
Cook for another minute or two. Add mushrooms. Season vegetables with salt & pepper, and sauté until most of the liquid has evaporated from mushrooms.
Pour in chicken broth and water; bring to a boil.
Add potatoes. Reduce heat to medium and simmer for about 15 minutes or until potatoes are fork tender.
Scoop out about half the vegetables and about ½ cup of broth (less vegetables if you prefer chunkier soup), and puree in a blender. While blender runs, add ½ cup of half and half.
Return the puree to soup and stir well.
Bring the soup back up to a simmer until heated through.