Preheat the oven to 190°C (375°F), Gas Mark 5. Toss the potatoes and peppers in the olive oil with the thyme sprigs and season with plenty of salt and pepper. Tip into a large roasting tin and place in the oven for 20–25 minutes until tender. Meanwhile, combine the beetroot and carrot with the salad leaves and divide among 4 serving plates.
To make the dressing, put all the ingredients and a pinch of salt and pepper into a jar with a tight-fitting lid. Shake well to combine.
Remove the roasting tin from the oven and discard the thyme. Arrange the vegetables on to the plates on top of the salad leaves and drizzle with the dressing. Scatter over the walnuts, if using, and serve immediately.