In the base of your salad bowl, whisk together the lemon juice, apple cider vinegar, mustard, garlic and salt. Slowly add in the olive oil while whisking to combine. Dip in a leaf of arugula to taste the dressing and adjust with salt, olive oil or vinegar if necessary.
Preheat the oven to 425 degrees. Cut the delicata squash lengthwise and scoop out the seeds. Slice thin, about 1/8" to 1/4" wide, and add to a parchment paper-lined sheet pan. Peel and cut the shallot in quarters and add it to the sheet pan. Drizzle everything with a little extra-virgin olive oil and sprinkle with kosher salt. Spread out the squash and shallot so it's in a single layer on the sheet pan, adding a second pan if necessary. Roast on the top rack of the oven for 30 minutes.
Thinly slice the celery with a mandolin or a knife. Add to the salad bowl, reserving any celery leaves for garnish. Add the pomegranate seeds and set aside.
Once the squash has roasted and cooled, add it to the salad bowl along with the arugula and toss gently to combine.
Top the salad with whole parsley leaves and any remaining celery greens. Sprinkle with crunchy sea salt, such as Maldon, and serve.