Cook the bacon and then remove it from the pot, leaving the bacon grease in the pot.
Cook the onion, leek, garlic and celery in the bacon grease until soft, about 10-15 minutes over medium low heat. (If there's not enough grease, add a little oil.)
Add the broth and bay leaf and simmer another 10 minutes or so until the potatoes are cooked. Taste and add salt and pepper as needed.
Add the chilies, corn, half the parsley, half the chives and the reserved bacon. If you started with leftover cooked potatoes, add them here. Simmer five minutes, then remove from the heat and stir in the milk. Top with the remaining parsley and chives.