Cook edamame in a large pot of boiling salted water until tender, 3-5 minutes. Using a slotted spoon, transfer to a large bowl of ice water. Return water in pot to a boil and add peas; cook until heated through, about 1 minute. Transfer peas to bowl with edamame; let cool. Drain well.
Working in batches, pulse edamame and peas in a food processor until a coarse purée forms, about 30 seconds. Transfer to a medium bowl. Stir in juice and next 3 ingredients. Gradually stir in 3/4 cup oil; mix well. Stir in 1/4 cup cilantro and 1/4 cup mint. Season with salt and pepper. DO AHEAD: Can be made 2 days ahead. Cover and chill.
Transfer to a serving bowl; drizzle with oil and garnish with more herbs. Serve with endive spears.