Grilled sandwiches like paninis almost always have cheese in them, which is important both for taste and structure. The cheese works like glue to hold the bread together and keep the ingredients in place. You can make one without cheese, but it's logistically difficult (the insides fall out while cooking) and I find it a little empty without the texture filling all the gaps.
Are there some substitutes that will provide the same material benefit without being cheese? I've used roasted sweet potato to great success in quesadillas, but it's a very strong flavor that won't play well with a lot of sandwich types.