Combine pearl barley, smoked ham hock, salt, black pepper, and cold water in a large pot.

Bring the mixture to a boil over high heat.

Reduce heat to low, partially cover the pot, and simmer for 45 minutes.

Add the finely chopped leeks, celery, onion, and peeled, finely chopped potato.

Continue to simmer for an additional 30 minutes, or until the barley and vegetables are tender.

Remove and discard the smoked ham hocks.

While stirring gently, pour in the heavy cream.

Simmer to heat the soup thoroughly, being careful not to boil.

Season to taste with additional salt and pepper as needed.

Serve hot.