Preheat your oven to 400F. Rub each beet with a little bit of olive oil, then wrap it in foil. Place the wrapped beets onto a baking sheet. Bake for 45-60 minutes, or until the beets are tender enough to be pierced with a fork or knife. Allow the beets to cool for 15 minutes. Then, run them under cold water and slip off their skins (this should be easy to do). Chop the beets into 1-inch pieces and set them aside.
While the beets roast, bring a medium pot of water to boil. Use a steamer attachment to steam the carrots for 15 minutes, or until fork tender. Set the carrots aside.
Add the tablespoon olive oil to a medium sized pot over medium heat. Add onions and sauté till the onions are soft and clear, about 5 minutes. Add the garlic and cook for one more minute, stirring constantly. Add the farro and vegetable broth. Bring to a boil and reduce heat to a simmer. Cook, covered but with the lid just slightly ajar, till the farro is plump and all of liquid has absorbed. This should take 30-40 minutes.
Add the cooked carrots and beets to the farro. Whisk together the lemon dressing ingredients. Pour the dressing over the hot grains. Season to taste with salt and freshly ground black pepper, and serve warm.
Leftovers will keep in an airtight container in the fridge for up to 4 days.