Spoon the yogurt into a standard 9x13 or 9x9 casserole dish and spread to cover the bottom of the container. On an 18x24 sheet pan, place two one-gallon freezer bags half full of ice. Pat down to make a smooth surface. Place the casserole dish with the yogurt over the ice to keep the yogurt cool. The idea here is not to cook the yogurt; smoke it.
I use a gas grill for this process. Turn one set of burners on by about a quarter and leave the rest of the grill off. If using a charcoal grill, start 4-5 pieces of charcoal and arrange them together on one side of the grill. Place the yogurt sitting on ice, opposite of the fire on the grate above the fire. (Never directly on the fire.)
I'm fortunate enough to have a gas grill that has a dedicated smoking compartment. However, you don't need one like mine. You can make an aluminum smoking packet for any gas or charcoal grill with a lid. Just place any hardwood smoking chips into a self-fashioned square/rectangular piece of aluminum foil and poke a few holes in it. Place the wood chip packet over a lit burner or directly on a few hot coals and close the lid. The grill should not be hot and barely noticeable that it's going, but with plenty of smoke. Smoke the yogurt for about 15-20 minutes.
The yogurt should have an off-white tone (slightly highlighted yellow peaks). Taste to see if the yogurt has taken on the smokiness of the wood chips. Remove and take back inside to finish. Next, add the yogurt, the rest of the ingredients in a food processor (or blender) and pulse until the mixture is thoroughly combined.