Drain onions in a sieve set over a bowl for 2 hours. Press onions to release more juice, then transfer to a large bowl, discarding juice. Add ground meat, garlic, egg, bread crumbs, salt, pepper, turmeric, and paprika, and mix well. Divide meat mixture evenly into eighths and shape into 5" cylinders. Slide meat cylinders onto 8 large flat wide metal skewers, molding and flattening meat around skewer to make each kebab about 8" long, 1 1⁄2" wide, and 1⁄4" thick (or if not using skewers, shape meat into eight 8" × 1 1⁄2" × 1⁄4" rectangles). Set kebabs aside.
Preheat a charcoal grill if using metal skewers, or heat a grill pan without sides over medium-high heat for nonskewered meat. Meanwhile, heat a small skillet over medium heat for 2 minutes. Remove skillet from heat, add saffron, and swirl threads around until lightly toasted, about 30 seconds. Crush saffron with a mortar and pestle, then add 1 tbsp. boiling water and stir in butter.
Brush kebabs with saffron butter. Put skewered kebabs over medium-hot coals or on grill pan; if cooking kebabs without skewers, put them on grill pan. Grill kebabs until browned on each side and cooked through, 3–4 minutes per side. Brush kebabs with remaining saffron butter and sprinkle with a little sumac (if using).
Slide kebabs off skewers (if using skewers) and serve with Persian Steamed Rice, if you like.