Make the marinade.
Combine all ingredients in a bowl made of nonreactive material (such as stainless steel).
Set aside about 1/4 cup to use on the kabobs while they’re cooking.
Prepare the meat.
Use a meat tenderizer to pound on the chicken and beef before adding it to the marinade. In addition to tenderizing the meat, it will help it soak up the flavors.
Add the marinade and the tenderized meat to a sturdy, 1-gallon zip-top bag.
Be sure to allow as much air as possible to escape before sealing the bag.
Give the bag a good shake to ensure that every piece of meat gets coated with the yogurt marinade.
Place bag in refrigerator and allow the meat to marinate for 2 to 3 hours.
While meat is marinating, soak the wood skewers in water so that they won’t catch fire during cooking.
Prepare your charcoal fire.
If you’re using a smoker, follow the unit’s instructions for getting a low and slow fire going.
You’ll want the kabobs to cook at about 275 degrees—slightly higher than the temp you might use for smoking ribs or pulled pork.
If you opt to use your charcoal grill as a smoker, you’ll need a water pan (a simple, inexpensive foil cake tin will work).
Fill your chimney starter about one-third full with briquettes or lump charcoal.
When the fire has died down and the coal is covered with a thin layer of ash, add all the charcoal to one side of the grate.
Place your disposable foil pan on the other side and add about two to three cups of water to the pan.
It should take about 30 minutes to one hour for the coals to cook down to the proper temperature for smoking the kabobs.
When they’re ready, drop your prepared wood chips onto the coals, then position the cooking grate above the fire.
Note that it may be necessary to add more coals during the cooking process if the fire dies down too much before the kabobs are ready.
Remove meat from the marinade.
When the meat has spent enough time in the chicken kabob marinade, gather all your ingredients.
Discard the yogurt marinade, allowing the excess to drip off before adding the meat to the skewers.
Assemble the kabobs.
Thread the meat and vegetables through the skewers.
The most efficient way to do this is to start with beef, then a layer of onion, one layer each green and red bell pepper, then mushroom, then chicken.
Repeat the process with each skewer, adding additional layers if necessary.
Add the kabobs to the prepared grill.
For the meat to reach the desired flavor and consistency, the kabobs should cook for about an hour and a half.
Turn the skewers every half-hour so that the heat and flavor distributes evenly.
Use an instant-read thermometer to ensure that the chicken has reached an internal temperature of at least 165 degrees Fahrenheit.
Brush the kabobs with the additional marinade that you set aside earlier as needed to help maintain moisture and boost the flavors.
Remove meat from grill and sprinkle with the reserved sesame seeds.
Serve alongside basmati rice, or substitute brown rice cooked with a little extra-virgin olive oil.