Place the green splits into a colander or sieve and rinse with cold water. Discard any debris.
Dice the vegetables into 1/2 pieces and give the garlic a rough chop.
In a large soup pot over medium-high heat, saute the vegetables in olive oil or butter. When they begin to soften and the onions become translucent, add the split peas, ham bone, and 10 cups of water.
Stir to combine and bring mixture to a rolling boil. Partially cover the pot and continue to boil for 30 minutes, then remove the lid and simmer uncovered for an additional 30-45 minutes.
Meanwhile, prepare the toast. Butter the slices of bread and season with garlic salt. Add pinchful of Parmesan cheese and run under the broiler for 2-3 minutes. Let cool slightly before slicing. (Or leave whole for scooping soup!)
Remove ham bone.Reduce heat to low and puree mixture, using a submersion blender or food processor to desired consistency. (I used my blender.)
Serve hot with a dollop of sour cream and some cracked black pepper, along with the Parmesan-Garlic toast or croutons. (Tastes great in a sourdough bread bowl too!)