Pick over split peas and discard any damaged peas or stones. Rinse peas and drain.
In a soup pot over medium heat, warm the olive oil. Add onions, coriander, cumin, cardamom and ginger. Cook for 8 to 10 minutes, stirring occasionally until onions are soft.
Add carrots, stock, 4 cups water and split peas into pot, bringing to a boil. Reduce heat to low and simmer gently for 30 to 40 minutes until peas are completely soft.
Remove soup from heat. Let cool for 30 minutes.
Working in small batches, puree soup in a blender on high speed until smooth, about 2 minutes per batch.
Thin with water or stock if soup is too thick. Return soup to a clean pan. Season with salt and pepper.
Crush coriander seeds in a mortar and pestle, coffee grinder or a spice grinder until coarsely ground. If using a coffee grinder or spice grinder, pulse a few times only.
Place coriander and remaining 2 tablespoons olive oil in a saucepan over medium heat. Warm for 1 minute and remove from heat.
In a small bowl, stir together yogurt, cilantro and enough water to make a barely fluid paste. Season with salt.
To serve, reheat soup gently. Ladle soup into bowls, drizzle with oil and yogurt and garnish with 1 cilantro sprig per bowl. Serve.