Combine the first three ingredients in a small bowl and whisk together. Spread the mayo mixture on the insides of each roll.
On the bottom of each roll top with a slice of cheese, followed by a layer of roasted red bell pepper strips, a layer of ham, salami, capicollo, pepper rings, and top it with another slice of provolone cheese. Place the top on the roll on top and use a hot panini press or indoor grill to press the sandwich together for about 1 to 2 minutes. Enjoy warm.
If using a pan to make the panini: Heat the pan to medium heat and place the sandwich in the pan. Use another heavy pan and place it carefully on top of the sandwich to press it down. After 1 minute flip the sandwich over and press it down again with the heavy pan. Cook for just one more minute and then serve.