Make the Arepas: Add the cornmeal and salt to a medium bowl and stir in warm water. Whisk until no lumps remain and water is fully absorbed. Let the mixture sit for 5-10 minutes.
Divide the dough into 6 even pieces and roll each into a ball. Flatten each ball to create a disk about 1/2 inch thick.
Set a large (10 or 12 inch) heavy skillet over medium heat. Add a layer of oil (about 1/4 inch deep) and heat until oil is shimmering but not smoking. Add as many arepas as will fit without crowding the pan and fry for about 4-5 minutes on each side, until arepas are crisp on the outside, and brown in spots. Remove from pan and set on paper towels to drain.
Make the Pulled BBQ Chicken: Add oil to a medium skillet set on medium-high heat. When oil is shimmering, add onions and cook, stirring often, until onions are soft and just starting to darken. Sprinkle in the garlic and cook for 1 minute. Add the barbecue sauce and heat until simmering. Tip in the pulled chicken, stir to coat with the sauce and cook until heated through. Taste, and add vinegar and honey to taste, if needed.
To assemble: Cut the arepas in half horizontally (as you would an English muffin) and add shredded cheese and about 1/4 cup pulled chicken. Top with avocado and pickled onions. Top with other half of arepa and serve warm.