Heat a large stock pot over medium heat. Add the shallots and cook until fragrant and soft, 5 to 6 minutes. Stir in the garlic and ginger, cooking for one more minute. Next, add in the curry paste, cooking for another minute.
Measure in the stock and water. Bring to a boil, add the split peas, reduce heat to low, and let cook for 35 minutes.
After 35 minutes, stir in the carrots and cook for another 10 to 15 minutes until the split peas and carrots are soft. Add the coconut milk, and simmer for another 5 minutes.
Taste and add salt as needed. Remove from heat and serve with cilantro and scallion greens if desired.