How to Make It
Preheat the oven to 400°. On a foil-lined baking sheet, toss the tomatoes with the garlic and 2 tablespoons of the olive oil and season with salt and pepper. Roast for about 25 minutes, stirring occasionally, until the tomatoes are golden and some have burst. Transfer the baking sheet to a rack to cool. Chop the garlic.
Meanwhile, in a large saucepan of salted boiling water, cook the farro until tender, 12 to 15 minutes. Drain well.
Preheat a grill pan. Brush the cut sides of the limes with oil and arrange them cut side down on the pan. Cook over moderately high heat, rotating occasionally, until charred, about 5 minutes. When the limes are cool enough to handle, squeeze them into a large bowl (you should have about 1/4 cup of juice). Add the shallot and chopped garlic and gradually whisk in the remaining 1/4 cup of olive oil until well blended. Season with salt and pepper. Add the farro, cucumber, arugula, parsley and mint and mix well; season with salt and pepper. Fold in the tomatoes and serve.