Cook the barley according to package instructions (it should take 30-45 minutes).
While the barley simmers, preheat your oven to 400F. Line two baking sheets with parchment or foil. Place the radicchio and corn on one sheet and drizzle with 1 tablespoon olive oil, salt, and pepper. Mix with your hands to coat the vegetables. On the other sheet, place the cherry tomatoes, halved side up. Drizzle them with the remaining tablespoon olive oil and give them a pinch of salt and pepper, too. Place the vegetables in the oven. After about 10 minutes, give the corn and radicchio a stir. After 20 minutes--or when the radicchio and corn are turning golden and the tomatoes are soft--remove all vegetables from the oven.
While the vegetables roast, place the vinegar and maple syrup or sugar in a small saucepan. Bring to a boil and then reduce the heat to low. Simmer, uncovered, for 10 minutes, or until the vinegar has thickened and has the consistency of a loose syrup.
Place the cooked barley and roasted vegetables in a mixing bowl. Add the balsamic glaze. Toss the ingredients to combine. Add the basil and season to taste with salt and pepper. Serve.
Notes
Salad leftovers will keep in an airtight container in the fridge for up to 3 days.