This is a link to the post where I have pictures and descriptions of what I did. Recipe credit NY Times. I made my own changes.
1 ½ cups small lentils, such as Pardina or Puy (12 ounces), or use any size green or brown lentil
2 bay leaves
Kosher salt and black pepper
4 or 5 medium potatoes, peeled and cut into bite sized pieces
3 tablespoons extra-virgin olive oil, plus more for drizzling
2 medium leeks, white and tender green parts, chopped in 1/2-inch pieces
1 medium, chopped, onion
3 links sausage (optional)
1 teaspoon chopped garlic (or more)
1 large thyme or rosemary sprig
2 tablespoons smoked sweet paprika
1/4 teaspoon ground cayenne, or to taste (I used a lot more)
1 cup chopped canned tomato with juices
2 tablespoons sherry vinegar (or more to taste – I used twice as much)
Rinse lentils. Put them in a pot and add 8 cups water and bay leaves. Bring to a boil over high heat, add a large pinch of salt, then reduce heat to a simmer. Cook with lid ajar for about 20 minutes. Add potato pieces and cook 15 more minutes. Turn off heat. Do not drain.
Put 3 tablespoons olive oil in a large soup pot over medium-high heat. When the oil is wavy, add leeks, chopped onion and optional sausage and stir to coat. Season with salt and pepper. Let cook, low heat, covered, until cooked, about 5 to 8 minutes. Turn heat to medium, stir in chopped garlic, thyme, paprika and cayenne. Stir 1 minute, until fragrant.
Add the chopped tomato. Let everything simmer for a few minutes. Pour potatoes and lentils, along with the cooking water, into the pot. Add more water if needed.
Bring to a boil, then reduce to a simmer. Cook covered with lid ajar for about 20 minutes. Add vinegar. Taste and adjust seasonings. The lentils will be quite soft and the potatoes will start to break. Discard bay leaves and herb sprig.
Finish with a drizzle of extra-virgin olive oil and serve.
To reheat leftovers add water as needed if too thick.