Preheat oven to 450 degrees F.
Cut potatoes into quarters, cover with water, salt the water, and bring to a simmer. Simmer until tender and drain, letting all the steam evaporate. When dry and cool, toss with 4 ounces extra-virgin olive oil and season with salt and pepper, to taste. Place in a single layer on a roasting pan and roast for 30 minutes until tender and golden brown. The potatoes will need to be stirred while roasting to insure all sides are nicely browned.
While potatoes are roasting, "shave" the fennel using a mandoline or the slicing side of a box grater. Thinly slice celery stalks and tops. Reserve.
Make the vinaigrette: In a large bowl, whisk together the Dijon mustard, vinegar, and salt, to taste. Gradually whisk in the remaining 4 ounces extra-virgin olive oil. Fold in fennel seeds and season with salt and pepper, to taste.
Remove roasted potatoes from oven and allow to slightly cool. Add potatoes and their oil to the vinaigrette bowl. Top with shaved celery and fennel and toss.