Place the farro in a bowl with 3cups (24fl oz/750ml) water and let stand at room temperature for 2 hours.
Simmer the farro
Drain the farro and place in a saucepan. Add the broth and bring to a boil over medium-high heat, then reduce the heat to medium-low, cover, and simmer until the farro is tender, about 30 minutes. Let stand, covered, for 10 minutes. Transfer to a bowl and let cool to room temperature.
Assemble the salad
Add the tomatoes and cheese to the farro. In a small bowl, whisk together the vinegars, 1teaspoon salt, and ⅛teaspoon pepper. Whisk in the oil until smooth. Pour over the salad, add the basil, and toss with a fork. Spoon into bowls and serve.