Heat oil in a large saucepan over medium heat. Add onion and carrot; sauté 5 minutes. Stir in 1/4 teaspoon salt and garlic; sauté 1 minute.
Remove half of onion mixture to another large saucepan. Add yellow peas to 1 pan; add 1/8 teaspoon salt, 1 1/2 cups water, 1 1/2 cups broth, and 1 1/2 teaspoons soy sauce.
Add green peas, remaining 1/8 teaspoon salt, remaining 1 1/2 cups water, remaining 1 1/2 cups broth, and remaining 1 1/2 teaspoons soy sauce to onion mixture in second pan. Bring both pans to a boil; cover, reduce heat, and simmer 45 minutes or just until peas are tender. Stir 1/8 teaspoon pepper into each pan. Cool slightly.
Pour yellow pea soup into blender; process on low speed until smooth. Return to pan. Repeat procedure with green pea soup, returning to other pan. Carefully pour about 2/3 cup each of yellow pea soup and green pea soup into individual bowls at the same time, so that soup pours evenly from each side, creating 2 colors in each bowl.
Combine sour cream and buttermilk; stir well with a whisk. Drizzle sour cream mixture over each serving. Garnish with chopped chives, if desired. Serve immediately.