Preheat the oven to 300° F.
Cut each roll into quarters; place onto a large baking sheet and drizzle with a touch of olive oil, salt, and pepper. Bake for 5-10 minutes, until crisp and lightly toasted. Allow to cool.
In a large bowl, whisk together the pickle brine, olive oil, and sugar.
Add the pickles and onion and toss well; season with salt and pepper, to taste. Add the arugula, basil and half of the shaved cheese; toss to combine. Lastly, add the toasted bread cubes; gently toss to combine.
Transfer the panzanella to a platter and top with the remaining cheese. Serve immediately.
Recipe adapted from: www.foodandwine.com