In a large soup pot or dutch oven, heat the 1 Tbsp of olive oil* over medium heat. Add the onions and sauté for 8-10 minutes. Add the garlic, salt, pepper, and oregano, and stir another minute.
Add the 8 cups of broth along with 1.5 cups of the split peas, reserving 1/2 cup to add partway through cooking.
Bring to a boil, then reduce heat and simmer, covered, for 40 minutes.
Add the rest of the dry split peas, chopped celery and carrots, and potatoes (if using).
Continue to simmer, covered, another 40 minutes, or until the peas are cooked and the vegetables are tender.
Add the liquid smoke and smoked paprika, and additional salt and pepper to taste. Partially pureé a few cups of the soup with a blender or immersion blender, or leave it chunky. Add broth or water to thin, if desired.
For an oil-free soup, dry sauté the onions, covered with a lid, and leave out the oil.