In a blender or food processor, blend juice with basil, mustard, and salt and pepper. Drizzle in olive oil. Season with salt and pepper as necessary. This dressing is meant to be thin and will lightly coat the salad.
For the Salad:
Wash and chop the greens, place in a salad bowl, and set aside.
Peel and open the pomegranate. Remove the seeds and put them in a separate bowl. Add a handful of the pomegranate seeds and half of the orange sections to the bowl of greens.
Pour dressing over the greens and mix it in with your hands.
Sprinkle the rest of the pomegranate seeds, the orange sections, radishes, and pecans on top of the salad.
Peeling pomegranates underwater (a full sink or big bowl will work) allows the seeds to sink and the pulp to float—and creates less of a mess, which makes everyone happier.