Cut the leeks in half lengthwise and rinse out any grit or sand. Dice the white parts and about 1 inch of the light green parts, then discard the tougher green leaves. Peel the potatoes and cut them into 1-inch dice, then add to a bowl and cover with water so they don't turn brown.

Melt 4 tablespoons of butter in a large pot over medium. Add the leeks and cook for 15 minutes or until soft and fragrant but not browned, stirring occasionally. Sprinkle the leeks with the flour and stir to coat.

Drain the water from the potatoes then add to the pot with the chicken broth, half-and-half, and the bay leaf. Whisk well and bring to a boil then reduce to medium-low and simmer uncovered until the potatoes are easily pierced with a fork, about 15-20 minutes. Remove from the heat, season with salt, and let the soup stand until cooled slightly, about 5 minutes. Discard the bay leaf.

Transfer the soup mixture to a blender jar. Remove the center of the lid so the heat can escape (or it will explode when blending!). Cover the lid with a towel to avoid splatters and blend the soup until smooth. If you like your soup chunky, reserve 2 cups of the soup before blending then add it back to the blended portion. Add the soup back to the pot to warm over medium-low (do not boil or the broth will break up.) If the soup is too thick, add more half-and-half, milk, or cream. Season with more salt if needed and serve with freshly ground black pepper, a drizzle of heavy cream or thinned sour cream, and minced chives.