Muffuletta bread roll: weigh and add all your ingredients to a large bowl or the bowl of your stand mixer. If you are kneading with a mixer, mix on medium speed for 8 minutes. If you are kneading by hand, you must knead it for around 10 or 15 minutes to get a smooth dough. 

Add dough to a lightly oiled bowl and place it in a warm spot in your kitchen. Allow to rise for 1 to 1.5 hours.

After the dough has more than doubled, remove it from the bowl and attempt to shape it into a smooth, round ball. With your hands or a rolling pin, flatten that ball into a flat disk shape that is less than an inch thick and about 8 to 9 inches in diameter. Carefully move this disk to a parchment-lined sheet pan. Cover the dough with a piece of plastic wrap and allow it to rise again for another 30 to 45 minutes. 

Near the end of the final rise time, preheat your oven to 400 degrees F (204 C). 

Remove the plastic wrap from the dough. Create an egg white wash by adding an egg white and 1 tablespoon of water to a small bowl. Whisk to combine. Paint the top of your dough very well with the egg white wash. Once the dough is fully painted in egg white wash, sprinkle a liberal amount of sesame seeds on top.

Bake the bread for 25 to 30 minutes, rotating the pan 180 degrees at the halfway point.

Allow bread to cool fully before slicing.

Olive salad mix: combine olives, roasted red peppers, garlic, capers, giardiniera, and parsley in your food processor. Pulse the blade three or four times and check the consistency. You may want to go a few more pulses. You want to still have visible pieces of each component; you do not want a paste or a puree. So just make sure to use a spoon and check the consistency while intermittently pulsing.

Once the consistency is to your liking, add everything from the food processor to a large bowl and add the olive oil and red wine vinegar. Stir to combine everything well. Store this olive salad mix in a sealed container in your refrigerator for up to a month. 

Sandwich assembly: slice the muffuletta roll. Drizzle the top bun with olive oil and red wine vinegar.

Add olive salad mix to the bottom roll. The goal is to have a consistent layer of olive mix on the bottom roll. It doesn't need to be thick, just consistent.

Add slices of mortadella, salami and ham. 

Top the meat with slices of cheese and then add the olive oil and red wine vinegar drizzled top bun to complete the sandwich.

Wrap this sandwich in plastic wrap or parchment and store in the refrigerator for up to two days. You can eat the sandwich immediately after you put it together, but at least one hour in the fridge will help the oils and vinegar saturate the bread, meat, and cheese and makes a better sandwich experience.