You can cook this dish on the stove or on a grill heated to medium-high.
Bring a small pot of water to a boil. Add basil; cook 10 seconds. Transfer basil to a bowl of ice water, then drain, and squeeze dry. Puree basil, 1/4 cup oil, and 1/2 teaspoon salt in a blender or food processor until smooth.
Heat remaining oil in a skillet over medium-high heat. Add scallions and garlic; cook until fragrant, about 30 seconds. Add corn, edamame, and remaining salt. Cook, stirring, until starting to caramelize, about 10 minutes (reduce heat to medium if overbrowning). Add tomatoes and vinegar; cook until tomatoes start to collapse, about 8 minutes.
Drizzle basil oil on vegetables, and stir. Serve immediately.
A New Skillet Set For a fresh update on succotash, replace lima beans with edamame.