In a large bowl, combine the onion, cumin and paprika. Crumble lamb over mixture and mix well. Shape into eighteen 1/2-in.-thick mini patties. In a large skillet, cook patties in oil in batches over medium heat for 3-4 minutes on each side or until a thermometer reads 160° and juices run clear.
On a lightly floured surface, unfold puff pastry. Roll each sheet into a 12x12-in. square. Cut each into nine squares. Place a burger in the center of each square; top with cheese. Lightly brush egg over edges of pastry. Bring opposite corners of pastry over burger; pinch seams to seal tightly.
Place seam side up on a 15x10x1-in. baking pan; brush with egg. Bake at 400° for 18-22 minutes or until pastry is golden brown.
Place sauce ingredients in a food processor; cover and process until blended. Serve with bundles.