In a large pot, heat some olive oil over medium heat. Add the chopped onion and garlic, and sauté until fragrant.
Add the sliced chorizo sausage to the pot and cook until browned.
Add the diced potatoes and chicken or vegetable broth to the pot. Bring to a simmer and cook until the potatoes are tender, about 15-20 minutes.
Using a potato masher or immersion blender, partially mash the potatoes in the pot to thicken the soup.
Add the sliced collard greens to the pot and simmer for another 5-10 minutes until the greens are wilted.
Season with salt and pepper to taste.
Serve the Caldo Verde hot, drizzled with a bit of olive oil and enjoy!