Thinly slice the beetroot on a mandoline and arrange in a shallow container.
Mix together the extra virgin olive oil, lime juice and vinegar, then season, to taste, with salt and freshly ground black pepper. Pour the mixture over the beetroot, cover and chill for 30 minutes in the fridge.
When ready to serve, heat the olive oil in a pan. Season the halloumi with salt and freshly ground black pepper and fry for 2-3 minutes on both sides, or until golden-brown all over. Remove from the pan and drain on kitchen paper.
To serve, arrange a ring of beetroot on each of four serving plates, then top the beetroot with the halloumi. Sprinkle over the capers and top each plate with a small handful of baby rocket.