Heat oven to 425 degrees. Drizzle beets with olive oil and roast in parchment-lined foil until tender, about 1 hour. Let cool, then peel and slice.
On a baking sheet, toss edamame with 1 teaspoon olive oil; season with salt and pepper. Roast, shaking pan once, until golden, 20 to 25 minutes.
In a small bowl, whisk vinegar and 2 tablespoons olive oil. In a medium bowl, combine arugula, basil, beets, and edamame. Toss with dressing and season with salt and pepper.