Heat oil in heavy large pot over medium-high heat. Add leek and bay leaf. Saute until leek wilts, about 3 minutes. Add split peas and stir to coat. Add 5 1/4 cups broth; bring to boil. Reduce heat to medium-low. Cover and simmer until split peas are just tender, about 35 minutes. Remove from heat. Transfer 1 cup soup solids, bay leaf, and remaining 1/2 cup broth to blender. Add petite peas and 4 tablespoons dill. Puree until smooth. Return puree to soup. Season to taste with salt and pepper. Ladle into bowls. Sprinkle with remaining 1 tablespoon dill.