Add the arugula leaves to a medium bowl. Core and slice the pear into 1/8-inch thick slices and add to arugula.
In another small bowl, whisk together vinegar, mustard, olive oil, and shallot. Season with salt and pepper.
Toss the arugula and pears with the dressing. Divide the salad between the plates and top with the toasted walnuts. Serve immediately.