Step 1

In a large Dutch oven or other large, heavy-bottomed, lidded pot over medium-high heat, heat the oil until it shimmers. Add the sausage and cook, stirring occasionally, until browned all over, about 4 minutes. Using a slotted spoon, transfer the sausage to a plate. Add the onions, garlic and a pinch of salt to the pot and cook, stirring, until the onion softens and starts to brown, about 5 minutes.

Step 2

Add a little of the broth and, using a wooden spoon, scrape up any browned bits that have stuck to the bottom of the pot. Add the remaining broth and the potatoes along with another pinch of salt. Increase the heat to high and bring the soup to a steady simmer. Reduce the heat to keep it at a simmer, cover and cook for 20 to 25 minutes, or until the potatoes are fork-tender and starting to fall apart.

Step 3

At this point, if you would like a chunky soup, you can add the kale and cook it until it softens and turns deep green, 5 to 10 minutes.

Step 4

If you prefer a smooth soup, remove the pot from the heat and use an immersion blender to blend the soup just until it is as smooth as you’d like. (Alternatively, you can puree the soup in batches in a blender: To prevent splatters, be careful to not fill it more than halfway, remove the center ring from the lid, and hold a kitchen towel over the lid as you blend.) Don’t blend the soup for too long, or it may become gluey.

Step 5

Return the pot to medium-high heat, add the kale and cook until silky and deep green, 5 to 10 minutes.

Step 6

Return the browned sausage to the pot, and simmer for another 5 minutes. Season the soup to taste with salt and pepper. Ladle into bowls, top with more black pepper, if desired, and serve hot.