Finely chop onion pieces in a food processor. Place a fine metal mesh over a bowl to strain the processed onion (press) and discard the juice.
Add the onion pulp to a medium bowl and the ground beef and lamb, mixed garlic, salt, spices, and egg.
Knead all ingredients together for several minutes until the mixture is paste-like and sticks to itself.
Fill a small bowl with tap water to wet your fingers as you make the kabobs.
Divide meat into 10 balls, then, taking one ball in hand, place on top of a 1-inch skewer and squeeze meat around until it is ½-inch thick. Leave the top and bottom of the skewer clear. Once finished, set gently over a shallow baking sheet. Repeat for all 10 kabobs.
Prepare the vegetable kabobs by tossing the vegetables in olive oil and placing them in various orders on thin skewers.
To Grill Kabob Koobideh: Take two square metal pipes and place them parallel to each other on the top and bottom of the cooking grate lengthwise. Place the tip of the skewers on the top pipe and the handle on the bottom to prevent the meat from sticking to the grate and falling off. Prepare the grill; it will be ready when the coals are grey and covered in ash!
Since vegetables take longer to grill, start with vegetables and add the meat kabobs halfway through.
Arrange as many skewers as possible on the grill. As soon as the last kabob is placed, begin turning the skewers in the order they were placed. This firms the meat on all sides and ensures they do not fall off the skewer. Continue turning until they are done, ideally with a nice grilled colour on the outside and no pink inside while maintaining juiciness. This will not take long!
Once finished, take meat and vegetable kabobs off the grill and wrap them in aluminium foil until it is time to serve them.
When serving, take a large piece of flatbread and use it like a mitt to pull the kabobs off the skewer and onto the serving platter. Once all kabobs are plated, brush melted butter over them.