Make the dressing: In a small bowl, whisk together the lemon juice, honey and garlic. Whisking constantly, slowly pour in the olive oil until all ingredients are incorporated. Season with salt and pepper. Toss with the arugula.
Make the breadcrumbs: Place the sourdough into a food processor and pulse until you have 3 cups of crumbs the size of large peas. Pour breadcrumbs into a bowl and coat with olive oil and lemon zest. Season with salt and pepper. Toast in a large frying pan over medium heat, moving the breadcrumbs around for even cooking, about 5-10 minutes, until browned and crispy. Toss with the arugula and top with shaved Parmesan cheese.