Whisk together the mustard and vinegar in a small bowl. Season with salt and pepper to taste. Slowly add the oil in a thin stream, whisking constantly until fully emulsified. If the dressing breaks while you're making it, stop pouring the oil and whisk what you've made so far until it comes together again.
Spread the arugula on a large platter. Slice off the top and bottom of each orange. Cut away the peel and outer membranes, then slice the orange cross-wise into wheels. Layer the orange slices over the arugula, followed by the fennel, onion (add more to taste) and basil. Season with salt and pepper. Pour the vinaigrette on top, toss and serve immediately.
Adapted from "One Dish at a Time: Delicious Recipes and Stories from My Italian-American Childhood and Beyond" by Valerie Bertinelli © Rodale 2012. Provided courtesy of Valerie Bertinelli. All rights reserved.