Preheat oven to 350 degrees F (175 degrees C). Lightly oil a 9x13-inch baking dish. Line with parchment paper that extends up the sides. Turn the parchment paper over so the oiled side is up.

Place ground lamb and beef in a mixing bowl. Add onions, garlic, rosemary, oregano, salt, pepper, cumin, paprika, cinnamon, cayenne pepper, and bread crumbs. Mix until well combined. Transfer to prepared baking dish and press the meat mixture firmly into the dish in an even layer that extends to the edges. Meat mixture should be packed and fairly dense.

Bake in preheated oven until nicely browned, 40 to 45 minutes. An instant-read thermometer inserted into the center should read at least 160 degrees F (70 degrees C). Cool to room temperature. Transfer to a plate. Cover with plastic wrap and refrigerate until chilled, 1 to 2 hours.

Transfer meat to a cutting board. Cut into 3 pieces crosswise. Slice each piece into 1/8-inch thick slices as you need them.

Heat oil in a skillet over medium-high heat. Cook slices until browned, about 2 minutes per side.