For the tzatziki: Cook the beet in boiling water until soft. When cool enough to handle, peel and add to a blender. Puree with the sugar and butter.
Put the garlic and vinegar in a blender and blend until smooth. Shred the cucumber on a box grater. Put the cucumber shreds in a towel, squeeze to remove all the liquid and put in a bowl. Add the yogurt, garlic and vinegar mixture, chopped dill, and season with lemon juice, salt, and white pepper. Add enough beet puree until you reach a color you like.
For the sliders: Place a grill pan over medium heat or preheat a gas or charcoal grill.
Thoroughly mix together the lamb, mint, oregano, feta, cumin, onions, jalapeno, salt and black pepper. Form into 4 to 6 patties. Grill to desired temperature, place on a bun, and top with the tzatziki.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.