Preheat oven to 400℉. Grease 2 baking sheets with cooking spray.
Cut square wonton wrappers in half to make triangles and spread out in a single layer on baking sheets. Spray with cooking spray and sprinkle with ½ teaspoon salt. Bake 6 to 8 minutes or until golden brown and crispy.
Meanwhile, combine edamame, cilantro, sesame oil, remaining ½ teaspoon salt, and lime juice in a food processor and pulse to chop. With processor running, slowly add olive oil and puree until smooth, about 5 minutes, adding enough oil to reach a smooth consistency.
Transfer dip to a bowl and serve with wonton chips.