Preheat your propane grill to 350 degrees.
Slice the top of the onion off but leave on the large stem.
Peel the onion's outer skin off.
Slice the onion into four sections through to almost the stem on the bottom. Slice those four sections into four sections. (You should have eight sections now, but you may prefer to slice them even thinner again.)
Use your fingers to carefully separate the onion sections to get that "bloom" affect without removing any of the onion sections.
Transfer to a square of foil slightly larger than the diameter of the onion.
Add bouillon, barbecue sauce, and Cajun seasonings inside the onion's sections.
Drizzle on top with olive oil.
Place on a hot grill and allow to cook for 15 minutes.
Sprinkle with cheese and grill another 5 minutes.
Remove transfer onion from foil to a plate and serve hot.