Heat oil in a large pot over medium high heat. Add onion and garlic, and cook, stirring periodically until softened, approximately 4 minutes.
Add potatoes and broth. Bring to a boil then reduce heat and simmer until potatoes are soft, about 15-20 minutes.
Meanwhile, heat a medium sized skillet over medium heat. Add chorizo or linguine and cook until browned, approximately 3-4 minutes on each side.
If desired in the same pan, saute' 2 slices of bacon that have been cut into 1/2 inche pieces.
Transfer chorizo to a cutting board. When cool enough to handle thinly slice on the diagonal crosswise. Transfer bacon to a paper towel to drain.
Puree soup with a hand blender or in a regular blender in batches. Do not fill more than halfway if using a blender.
Return to pot and stir in greens, simmer additional 5 minutes.
Season with salt and pepper to taste.
Serve soup drizzled with oil and topped with chorizo and bacon.
Optional garnish with cilantro if desired.