"Arepas are small grilled corn cakes and are native to Venezuela and Colombia. They can be eaten plain or stuffed with meats, cheeses, beans and vegetables. Sugar can be added to create a sweet cake which can be used for dessert."
Bring milk to a simmer in a pot. Remove from heat and stir in butter.
Combine arepas flour, grated Monterey Jack cheese, kosher salt, and black pepper in a large bowl. Add the hot milk mixture and honey; stir until combined. Let mixture sit until milk is absorbed enough for a soft dough to form, 1 to 2 minutes. Dough will continue to stiffen.
Form dough into 12 balls about 2 inches in diameter. Flatten between palms into 3 1/2- to 4-inch arepa patties about 1/3-inch thick.
Heat oil in a large nonstick skillet over medium heat. Fry 3 to 4 arepas at a time until lightly golden brown, about 3 minutes per side. Slice each arepa in half crosswise and stuff a portion of chicken, sliced Monterey Jack cheese, and avocado between the halves.