Preheat the oven to 425 degrees F.
For the dressing: In a bowl, whisk all dressing ingredients (lemon juice through black pepper). Set aside.
Toss the broccoli with the olive oil, coating all of the florets, and spread them out in a single layer on a baking sheet. Sprinkle evenly with the salt. Roast for 25 minutes, until tender and browned.
While the broccoli roasts, make the farro. In a small saucepan, combine the farro with 3 cups water. Bring to a boil, stir, then reduce the heat to low and simmer until the grains are tender but still chewy, 20 to 25 minutes. Drain off the excess water and fluff the farro with a fork. Transfer to a large bowl and let cool slightly. Stir in the lemon dressing to coat all of the grains. Stir in the roasted broccoli, flaked tuna, and Parmesan. Taste and season with more salt and pepper if desired.