Preheat the oven to 220°C.
Place each beetroot on a piece of foil. Drizzle with a little of the olive oil, season with salt and pepper, and wrap securely. Place on a baking tray and roast for approximately 50–70 minutes, depending on their size, or until a small sharp knife passes easily through the centre.
Allow the beetroot to cool enough to handle, then gently rub away the skins and cut the flesh into medium-sized pieces.
While the beetroot is roasting, place the carrots on a separate baking tray. Drizzle with the remaining olive oil and season generously with salt and pepper. Toss well, then spread the carrots into a single layer.
Roast for 25–30 minutes, turning once or twice, until tender, golden and slightly crisp around the edges.
Meanwhile, bring a large saucepan of water to the boil and season it generously with salt. Add the farro and cook according to the packet instructions, or for approximately 25–30 minutes, until tender but still pleasantly chewy.
Drain the farro well and transfer it to a large serving bowl.
To make the dressing, place all the ingredients in a bowl and whisk until smooth and combined. Alternatively, place them in a jar, secure the lid and shake well. Taste and adjust the seasoning as needed.
Add half of the dressing to the farro while it is still warm and toss well. Allow it to cool slightly.
Add the roasted carrots, beetroot, rocket and fresh herbs. Gently toss everything together, taking care not to break up the beetroot too much.
Transfer to a serving platter or bowl. Scatter over the toasted nuts and the feta or goat’s cheese, if using. Drizzle with the remaining dressing and serve warm or at room temperature.