In a large bowl, combine the lamb, beetroot, egg, mint, and garlic. Season to taste with salt & freshly ground black pepper and mix thoroughly.
Divide into 4 equal portions. Take one portion and flatten it in the palm of your hand. Place a cube of feta in the middle and draw the meat up and over the cheese, molding it into a burger shape and taking care to ensure the cheese is totally surrounded. Repeat with the other meat portions and set aside in the fridge for 30 minutes to rest.
When you are ready to cook the burgers, heat a griddle pan (or BBQ) to medium hot and cook the burgers for around 6-8 minutes on each side. Check they are cooked by inserting a skewer into the middle. If it comes out piping hot to touch they are cooked, if not cook for a further minute or so.
Serve the burgers in buns with salad.
Note: Preferable to use Ruby red baby beetroot, freshly cooked and infused with a natural marinade made using chili, oil, a little sugar, and white wine vinegar. This adds a delicious kick to salads and spices up cold meats and sandwiches.