Dice the onion and mince the garlic. Cook them in a large stock pot over medium heat with the olive oil until soft. Add the chopped carrots and celery and cook a few minutes more.
Add the ham hock and peas to the pot. Add the chicken broth and bay leaf to the pot. Bring the mixture up to a simmer with a lid on then reduce the heat to low and let simmer for 1 hour.
Dice the potato into small chunks, add to the pot and continue to simmer until the potato chunks are soft (about ten minutes). The peas should have completely disintegrated by this point as well. If they are still retaining their shape, continue to simmer until they are mush (see photo below).
Remove the bay leaf and ham hock. Transfer 1/3 to 1/2 of the soup to a blender and puree until smooth. Return it to the pot and mix it in with the rest of the soup. Remove the meat from the ham hock, cut it into small pieces and return it to the pot. Taste the soup and adjust salt and pepper to taste!