Heat olive oil (or a small amount of water) in a large pot or dutch oven over medium heat. Add onions and garlic and cook until onions are translucent (approx. 5 min.). Add curry paste, water, split peas, and carrot. Stir and bring to a boil. Reduce heat to a simmer, cover and let cook , stirring occasionally, until split peas are fully cooked and soft (approx. 50 - 60 min.) Turn off heat and let soup cool slightly.