Combine the bbq ingredients in a mason jar and shake until fully mixed.
Turn on the bbq and let it heat up a bit, then set it at about mid-temp.
Toss the kohlrabi wedges, oil, and barbecue sauce together in large mixing bowl until evenly coated. Spread the kohlrabi on the grill; close the lid and cook for about 7-10 minutes, flip and cook for about 6-8 more minutes, checking for doneness several times during the final 5 minutes of cooking. There should be a slight char/caramelization on the outside, and the kohlrabi should be crisp-tender on the inside.
Transfer to a serving bowl; season with the pepper. Let cool a few minutes before garnishing with the green onions (or, if you're making this in advance, wait to add the chives until after you've reheated the kohlrabi). Serve warm or at room temperature.