Finely chop the onion and garlic. In a mixing bowl, combine the ground lamb with the ground cumin, cinnamon, Hungarian sweet paprika, salt, and pepper.
Heat olive oil in a skillet over medium heat. Add the spiced lamb mixture and cook for 7-8 minutes, or until cooked through and lightly browned.
Meanwhile, prepare the fresh ingredients: thinly slice the cucumber and tomato, and finely chop the fresh mint.
In a small bowl, mix the Greek yogurt with the chopped mint, a pinch of salt, and pepper.
Warm the tortilla wraps in a dry skillet or oven for 1-2 minutes to make them more pliable.
Place a tortilla wrap on a clean surface, then spread a generous amount of the mint yogurt sauce over it.
Top with the cooked lamb, then distribute the cucumber and tomato slices evenly.
Carefully fold in the two sides of the tortilla, then roll it up tightly.
Cut the wrap in half and serve immediately with a fresh salad or extra yogurt sauce.
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