If needed, cook dry split peas. Rinse first, and add dry peas to a pot of boiling water. (Use 6-8 cups water for every 2 cups of peas.) Simmer gently with a tilted lid until desired tenderness reached, about 20-30 minutes. Drain excess water (if any) and serve or store in a covered container in the fridge for up to one week.
Heat oil in a large stock pot over medium-high heat. Add onion and cook until translucent, about 5 minutes. Add sweet potatoes and carrots, and cook, stirring occasionally, about 10-15 additional minutes. Add broth, garlic, ginger, turmeric, and salt and pepper. Bring to a boil, and then reduce heat to a simmer, and cook until vegetables are tender and soup is aromatic, about 20 minutes. Remove from heat.
Use an immersion blender to puree, or ladle the soup (in batches if needed) to a blender, and blend on high until smooth, about 2-3 minutes.
Divide pureed soup between serving bowls. Stir in cooked split peas, and top with chives, basil, and plain yogurt if desired. Store in the fridge for up to one week. Enjoy!