Heat 1 tbsp oil in a large pan over medium heat. Add onion slices and cook until slightly transparent. Add honey and a sprinkle of salt and cook until a dark caramel color, stirring often. 

Remove onions from pan and heat another 1 tbsp of oil. Add mushrooms and garlic and cook until mushrooms have a golden sear. 

In a food processor, combine feta, 2 tbsp olive oil, lemon juice, and salt and pepper. Pulse until smooth. 

Slice ciabatta rolls lengthwise and brush the outside of each side with oil. Spread the feta spread on one slice of each roll then top with 1/4 of the chicken, onions, mushrooms, and mozzarella. Repeat with remaining three sandwiches. 

Cook sandwiches on panini press on in a skillet until cheese is melted. Cut each sandwich in half and serve warm.