Wash the delicata squash and cut in 1/2 inch thick slices. Using a spoon, scoop out the seeds in each slice and discard.
Place the squash slices on a baking sheet and brush both sides with olive oil. Sprinkle with salt and pepper and place in the oven. Cook for 25 minutes, flipping 2-3 times with a spatula for even browning. Remove from the oven and set aside to cool.
In a small bowl whisk together all the vinaigrette ingredients.
In a large mixing bowl combine the arugula, pears, pomegranate, shallot and pepitas. Drizzle the dressing and toss to combine.
Serve immediately by plating one portion of salad with 2-3 slices of squash.
*Note: Arugula wilts fairly quickly. If you don't plan to serve the salad immediately, reserve the dressing and drizzle on an individual basis.