Heat olive oil in a soup pot over medium heat. Cook leeks for 5 to 6 minutes, stirring, until soft without browning.
Add potatoes, broth, bay leaf and pepper. Bring to a gentle simmer and cook partly covered for 12 to 15 minutes until the potato pieces are just tender.
Add ham strips and peas and simmer for 4 to 5 minutes until the peas are bright and the ham reaches 165°F. Avoid a hard boil that would break the potato pieces.
Discard bay leaf and remove from heat. Stir in lemon zest, lemon juice and parsley.
Taste before adding up to the measured salt, then divide among six bowls with potatoes, ham and peas in every portion.