Add oil to a 4-quart stockpot and heat over medium.
Add onions and garlic to the hot oil, then add oregano, salt, and pepper; sauté 5-10 minutes until the onions are translucent.
Stir in the carrots, potatoes, vegetable broth, and 1/2 the split peas.
Bring to a boil, then simmer uncovered for 40 minutes, skimming off the foam while cooking.
After 40 minutes, add the remaining split peas and continue to simmer for another 40 minutes, or until all the peas are soft. Stir frequently to keep the solids from burning on the bottom.
Season with additional salt and pepper to taste before serving.