Place split peas, water and chicken bouillon cubes into a large saucepan or soup pot (stainless steel is best). Bring the ingredients to a boil with medium-high heat, stirring occasionally. Once they come to a boil, turn down the heat to a low simmer; let the peas continue to cook for about an hour (or until the split peas become tender).

When peas are done, purée peas and liquid, using a stick immersion blender OR processing in batches using a food processor. If using food processor, return purée to pan.

Prepare pressure canner, jars, lids, etc. per manufacturer guidelines.

Add ham, carrots, onion, allspice and bay leaf to soup. Bring soup to a boil. Reduce heat to low and cook for 30 minutes. Season soup with salt and pepper, to taste. If soup is a bit too thick, you can thin it out a little by adding a bit of boiling water to pan. Stir to combine. Remove bay leaf.

Place hot, prepared jars on a dish towel. Ladle the soup mixture into jars, being sure to leave 1 inch headspace on each jar. Remove or add liquid, as necessary, to ensure correct headspace. Remove air bubbles from jars, then wipe the rim of jars clean using a wet paper towel, to ensure a good seal. Place hot flat lids on jar, then screw the bands into place until they are fingertip tight.

Carefully put the jars into water in prepared pressure canner. Lock lid; turn heat to medium-high. Once vent begins steaming, let it vent for 10 minutes, then close vent. Heat until canner reaches 10 pounds pressure. After it reaches 10 pounds pressure, process PINTS for 75 minutes and QUARTS for 90 minutes.

When done, turn off heat. Let the pressure in the canner drop to zero naturally. Once it gets to zero, wait a couple more minutes, then open the vent cover. Wait another 10 minutes, then carefully remove the canner lid. Place the hot jars on a dish towel on counter, and let them sit undisturbed for 24 hours. Check for proper seal, then label and store jars in pantry.