How to Make It
In a saucepan, heat the oil. Add the shallots and celery and cook over moderate heat, stirring, until softened, about 5 minutes. Stir in the barley, garlic and bay leaves. Add the apple juice and water and season with salt. Bring to a simmer; cover and cook over low heat until the water is absorbed and the barley is tender, 45 minutes. Spread the barley on a baking sheet to cool. Discard the bay leaves.
Preheat the oven to 425°. On a rimmed baking sheet, toss the cherry tomatoes with the oil, honey and garlic. Season with salt. Roast for 20 minutes, stirring, until soft and caramelized. Transfer the baking sheet to a rack.
In a large bowl, whisk the maple syrup with the apple juice and vinegar. Season with salt. Add the green tomatoes, toss to coat and let stand at room temperature for at least 30 minutes, stirring occasionally.
In a bowl, whisk the vinegar, oil, apple juice, honey, lemon zest and chopped tarragon. Add the barley and toss. Season with salt. Spoon into shallow bowls and top with the roasted cherry tomatoes and marinated green tomatoes. Garnish with tarragon leaves and serve.