Chop the leeks (watch the video!): Chop off the dark green stems of the leeks and the bottom root, then slice them in half lengthwise. Place each leek half cut-side down on the cutting board, then chop it into thin slices, resulting in half-moon shapes, then rinse them thoroughly in a colander. Dice the potatoes. Drain the beans.
Heat the olive oil and saute leeks 4 minutes until softened, then add the potatoes and saute for 2 minutes.
Add broth, water, ½ teaspoon kosher salt, and white beans. Bring to a boil, then simmer 15 minutes. In the last 2 minutes, stir in spinach, spices, and another 1 teaspoon kosher salt. Heat until the spinach is wilted. Puree in a blender or using an immersion blender. If the soup is too thick, add a few more tablespoons of water until the desired consistency is achieved (this may also be necessary when reheating). Serve garnished with chopped chives.