1 ½ cups small lentils, such as Pardina or Puy (12 ounces), or use any size green or brown lentil
1 medium onion, halved, plus 2 bay leaves and 2 whole cloves
Kosher salt and black pepper
4 or 5 medium potatoes, peeled and sliced 3/4-inch thick
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 teaspoon chopped garlic
1 large thyme or rosemary sprig
2 tablespoons pimentón dulce or smoked sweet paprika
⅛ teaspoon ground cayenne, or to taste
Small pinch of saffron (about 12 strands), soaked in 1/4 cup cold water
1 cup chopped canned tomato with juice
2 tablespoons sherry vinegar
Chopped parsley (optional)
Rinse lentils. Put them in a Dutch oven or large, heavy-bottomed pot and add 8 cups water. Pin a bay leaf to each onion half using a whole clove and add to the pot. 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 30 minutes, until soft. Turn off heat.
Meanwhile, bring a medium pot of salted water to boil, and cook the potato slices until just done, about 10 minutes, then drain and spread out on a baking sheet to cool.
Put 3 tablespoons olive oil in a large skillet over medium-high heat. When the oil is wavy, add leeks and stir to coat. Season with salt and pepper. Let leeks cook briskly, stirring frequently until soft but still bright green, about 5 to 8 minutes. Turn heat to medium, stir in chopped garlic, thyme, pimentón and cayenne.
Add saffron and soaking water, the chopped tomato and vinegar. Turn heat to high and let everything simmer for a few minutes. Pour contents of skillet into Dutch oven with lentils. Add the reserved potatoes.
Bring to a boil, then reduce to a simmer. Cook covered with lid ajar for about 10 minutes. Taste and adjust seasoning, then cook for 10 more minutes. The lentils will be quite soft and the potatoes will start to break. Discard onion and thyme sprig.
Finish with a drizzle of extra-virgin olive oil and chopped parsley, if you wish.