In a large pot, cook chourico or sausage over low heat. Turn and cook until brown, about 10 minutes. Remove from pot and let cool. Cut sausage into slices. Remove any fat from pot, but leave the cooked on bits.
Add oil to pot, add onion and cook on medium until translucent, about 5 minutes. Add garlic and cook 1 minute more. As you stir, scrape up the bits from the bottom of the pan.
Add broth potatoes, and black pepper, bring to a boil and cook 20 minutes. Remove the pot from heat and either lightly mash the potatoes with a potato masher or food processor, or I like to use my immersion blender to puree the entire mixture.
Add chourico or sausage, red pepper flakes and bring back to a simmer. Cook covered for about 4 minutes. Add kale and bring back to a simmer. Cook partially covered until the kale is cooked. Adjust salt if needed.