Heat 2 tablespoons of the olive oil in a medium saucepan over medium heat until shimmering. Add the shallots and sauté until translucent, about 5 minutes. Add the farro and toast, stirring to coat each grain, until fragrant, 1 to 2 minutes.
Add the broth and bring to a boil. Reduce the heat to maintain a simmer, cover, and cook until farro is soft but still chewy in the center, about 12 minutes. If there is more than a tablespoon or two of cooking liquid left, strain it out.
Transfer the farro to a large bowl and let cool to room temperature. Add the vinegar and remaining 2 tablespoons olive oil, and stir to combine. Add the tomatoes, cucumbers, and basil and toss to combine. Taste and season with salt, pepper, vinegar, and oil as needed. Serve chilled or at room temperature.
