In a large pot, drizzle olive oil over medium heat. Slice the Chouriço into 1/4 inch thick circles and add to hot oil. Fry until lightly browned, 3-5 minutes. Use a slotted spoon to remove sausage, keeping all the drippings in the pot.
Add the diced onions and sprinkle with salt. Cook, stirring occasionally, until softened and translucent. Stir in garlic slices and cook until fragrant, about 1 minute. Add the diced potatoes and cover with the water. Bring to a boil, then decrease heat to medium low. Simmer until the potatoes are fork tender, 15-20 minutes. Remove from heat.
Use an immersion blender (or carefully transfer to a blender) to puree the soup.
Slice the kale into strips as thinly as possible.
Bring the soup back to a boil, stir in the kale, reduce heat, and simmer until wilted, about 2 minutes. Season with salt and pepper.
Serve immediately with Chouriço.