Peel and thinly slice the onions. In a large pan, cook the onions in olive oil over low heat, add a teaspoon of apple cider vinegar half way through. It will take 15-20 minutes for them to fully caramelise. Turn the oven to full with the broiler on.
Make the sandwich spread by adding mayonnaise, horseradish and minced garlic to a bowl and stirring to combine. Cut the marinated red pepper into small pieces.
Spread the horseradish mayonnaise to the sliced ciabatta and add layers of roast beef. Top with the caramelised onions and marinated red pepper pieces. Place the cheese slices on top.
Place in the preheated oven under the broiler for 2-3 minutes, keeping a close eye to make sure that it does not burn. Remove when the cheese is melted. Add arugula and serve hot.