If making in a pressure cooker: If you are in a hurry, put the split peas in the pot with about 8 cups of cold water and start the fire. You can chop and add the vegetables as they get done.
Add the vegetables, bay leaf, ham hocks and enough water to cover by 2 inches.
When it comes to a simmer, close the lid on the pressure cooker; allow it to come to pressure. When pressure is reached, lower the heat to low, and allow to cook for 30 minutes. Turn off the heat; allow the cooker to cool naturally, about 5 - 10 minutes.
Uncover and check for doneness. Remove the ham hocks and set aside to cool. Allow the split peas and vegetables to just simmer on top of the stove for a few minutes until the peas are mere mush. (It's o.k. if the carrots still look like carrots, as a matter of fact, it's preferred). Add water if the soup seems too thick. Allow the ham hocks to cool until they don't burn your hands anymore, then, carefully cut, pull, or otherwise extract the meat from the bones. Chop the meat into little fine pieces and add back to the soup. Stir well. Taste and adjust the seasonings with salt and pepper to taste.
If making in the crockpot: Place the split peas, onions, carrot, and celery into the crockpot, add water to cover by 2 inches, then nestle in the ham bone or hocks. Cover and cook on high for 6 hours, or low for 8 hours. Once cooked, carefully remove the bone(s) and extract the meat when cool enough to handle. Return meat to the pot and taste and adjust seasonings with salt and pepper.
If making on the stovetop: Follow the directions for the pressure cooker, allowing about 1 ½ hours of simmer time.