Preheat the oven to 425 degrees. Spread the carrots, broccoli, and red onion on a baking sheet. Drizzle with 2 tablespoons olive oil and season with salt and pepper. Toss to coat, then roast for 25 minutes until the vegetables are tender and browned at the edges.

While the vegetables roast, bring a large pot of salted water to a boil. Add the farro and cook for 20 minutes until tender but still chewy. Drain and rinse under cold water to cool.

Toast the sliced almonds in a dry skillet over medium heat for 3 to 4 minutes, stirring often until golden. Set aside to cool.

In a large bowl, combine the cooked farro, roasted vegetables, and toasted almonds. Drizzle with the remaining tablespoon of olive oil and the balsamic vinegar. Add the chopped parsley and toss gently. Season with more salt and pepper if needed.