Broil or grill the jalapenos to char on all sides. Remove from heat and put them into a bowl. Cover with plastic wrap and allow to sit for 15 minutes.
Meanwhile, add the feta, onion, garlic, mint, cumin, and paprika to the bowl of a food processor.
On a cutting board, peel the jalapenos and remove the seeds. The skin should come off easily after resting in the covered bowl. If you want to turn up the heat you can leave some of the seeds.
Roughly chop the flesh of the peppers and add it to the food processor with the rest of the ingredients. Pulse about 15 times until everything is chopped up small.
Put the lamb into a bowl and pour the jalapeno-feta mixture over the lamb. Stir well to combine and use your hands if needed to really get everything mixed together.
Form the lamb into either burger sized patties, or long sausage shapes on skewers. Place them into the fridge for about an hour to firm up.
Preheat a grill to high. Brush the kofta with some oil. Grill on high heat until cooked through. Depending on your shape and size this could be anywhere from 5 to 10 minutes per side
Remove from heat, serve with tzatziki and garnish with fresh mint.