Preheat the oven to 375°. In a small baking dish, lightly drizzle the beets with olive oil and rub to coat. Cover with foil and roast for about 1 hour, until the beets are tender. Let cool, then peel the beets and cut into 1/2-inch dice.
Meanwhile, in a medium saucepan, combine the garlic, thyme, rosemary, water and 2 teaspoons of salt and bring to a boil. Stir in the farro and simmer over moderate heat until just tender, about 15 minutes. Drain well. Transfer the farro to a bowl and discard the garlic and herbs. Let cool to room temperature, stirring occasionally.
In a small bowl, combine the shallot, lemon juice and honey. Gradually whisk in the 1/3 cup of oil and season with salt and pepper.
In a medium bowl, toss 2 tablespoons of the dressing with the trout. Add the beets, greens and the remaining dressing to the farro and toss gently. Season with salt and pepper and let stand at room temperature for 20 minutes. Transfer the salad to a serving platter, scatter the trout on top and serve.