In the bowl of an electric mixer fitted with the paddle attachment, stir together the flour, yeast and salt. With the mixer on low speed, slowly add the warm water and then the oil and honey. Mix with the paddle attachment until the mixture starts to come together. Switch to the dough hook and let the mixer knead the dough for 10 minutes until a soft, smooth ball starts to form. If you don’t have a dough hook or an electric mixer, you can do this with your hands.
Meanwhile, in a large bowl, mix together the chicken, red onion and ¾ cup barbeque sauce. Set aside along with the cheese and cilantro.
Preheat grill to medium-high heat.
Divide dough into 4-8 pieces. Form each piece into a ball and then flatten into a round disc with your hands. Spread the dough with a thin layer of barbeque sauce, leaving a rim around the edge. Place ½ cup chicken mixture on one side of the dough. Sprinkle with cheese and a little cilantro. Fold the non-covered half of the dough over the filling and press the edges together with your thumb. Repeat with remaining dough and fillings.
Brush each calzone and the grill with a little oil. Grill the calzones for about 5 minutes per side until grill marks start to form and crust is crisp.