With a sharp utility knife, cut out a large hole from the top of the loaf and then, using your fingers, remove as much bread as possible from the inside, while being careful not to damage the crust. Tear about half of the bread you just removed (about 2 cups) into bite size pieces and place it in a large mixing bowl. You can discard the rest or save it for another usage.
Add the chopped bell peppers, parsley, kalamata olives and grated cheese to the bowl with the torn bread and set aside.
In a separate bowl, combine the olive oil, minced garlic, dried oregano, salt, pepper and cayenne and whisk vigorously until well combined.
Pour over the reserved bread stuffing and mix well.
Stuff this mixture into the hollowed out bread, compacting it really well as you go. Although it may seem like a lot of stuffing, if you do a good job at compacting it, you should have no problem fitting it all in.
Replace the "cap" on the stuffed bread, wrap it in aluminium foil and then place it in the refrigerator overnight, or at least for a few hours, to allow for flavors to develop.
Although this muffuletta can be eaten cold, I strongly recommend that you send it for a brief trip to the oven first before eating it. This will make the bread all warm and crispy, while leaving the stuffing real fresh and cold.
When you are ready to eat, preheat the oven to 400°F.
Open the foil about halfway and then place the loaf in the hot oven for about 15 to 20 minutes, or until the bread feels warm and crispy but the salad inside is still cold.