Heat the oven to 425 degrees, with the racks arranged in the center. Line 2 small rimmed baking sheets with parchment paper.
While the oven is preheating, put 2 tablespoon of the olive oil in a small saucepan. Place over medium heat and add the shallot, garlic, cumin, coriander and cayenne. Cook until the shallot is softened, stirring, about 5 minutes. Add the farro, water and 1 teaspoon salt. Bring to a simmer, then lower the heat and cover. Cook until the water is absorbed and the farro is tender, about 25 minutes.
Toss the eggplant, red onion, 2 tablespoons olive oil and 1 teaspoon salt on one baking sheet and season to taste with black pepper. Repeat with the tomatoes, 2 tablespoons olive oil and 1 teaspoon salt on the second baking sheet.
Roast the vegetables for 20 - 25 minutes, stirring halfway through. The eggplant should be softened and golden brown and the tomatoes juicy and wrinkled.
Transfer the farro to the baking sheets, dividing it equally. Spread it out on the pan and let everything cool 15 minutes.
When ready to serve, scrape the farro and the vegetables into a large bowl and add the lemon juice. Sprinkle the mint and feta over the salad and toss gently.
Tip: Enjoy the salad warm, at room temperature or keep it in the fridge to pack for lunch the next day.