Cook the quinoa in plenty of boiling water for 10-15 mins (don’t worry if it still has a little bite), then drain well and leave to cool. Grate the beetroot and mix with the yogurt, half the mint and some seasoning. Chill until ready to serve.
Use your hands to squish together the cooked quinoa, the lamb, the remaining mint, half the dill and some seasoning. Shape into four burger patties. Heat a large frying pan (if it’s non-stick, you won’t need oil as the lamb mince is already fatty; otherwise, add a drizzle of oil). Cook the burgers for 5-8 mins on each side until they have a nice golden crust and are cooked through, then leave them to rest for a few mins.
Mix the carrots, onions and the remaining dill in a bowl. Gently warm the wraps or buns, then pile with the carrot mix, add the lamb patties and top with a dollop of the beetroot tzatziki.