Prep the veg and shred the ham - Chop the scallions, separating the white from the green parts. Dice the carrots and celery. No need to peel the potatoes. Just chop them into bite-sized pieces. Shred the ham steak.
Simmer - Add the potatoes, shredded ham, 2 cups of corn kernels, bay leaf, and broth to the pot, and simmer until the potatoes are soft.
Blend the milk and reserved corn kernels - Blend the remaining 2 cups of corn kernels with the milk until there's no texture left at all. Strain if necessary.
Allow the chowder to thicken - Add the blended corn and milk mixture to the soup pot. This is when it becomes chowder! Cook for about 10 minutes longer, allowing the chowder to thicken a bit.
Garnish and serve - Remove the bay leaf. Stir in the scallion greens and the parsley, and serve with big spoons.