Preheat oven to 425ºF Line a rimmed baking sheet with parchment paper.
Make Shallot Chive Butter: Combine the butter, 2 tablespoons of chives, shallots and salt in a shallow bowl or on a cutting board. Use a fork to mix and mash and fold the chives, shallot and salt into the butter, until everything is combined. Transfer half the compound butter to a small saucepan and set aside. (note: You can make the butter ahead and store it, tightly covered, in the fridge, for up to a week or in the freezer for up to 3 weeks. Bring it to room temperature before using.)
Peel and slice the potatoes: Fill a large bowl halfway with cold water. Add vinegar. Peel potatoes, scraping a tiny bit extra off the bottom of each potato, with the peeler, to make a flat stable surface, so they don't roll around when you slice them. Place potatoes into the bowl of water, as you peel them, to prevent discoloration.
Cut The Potato into Hasselbacks Take a potato out of the water and dry it. Lay it, lengthwise, between two wooden-handled spatulas or two chopsticks. The wood on either side of the potato will prevent you from cutting all the way through. (see instructional photos in post) Make slices, about ¼ of an inch apart, along the entire length of the potato. Repeat with remaining potatoes. Place potatoes on baking sheet. Lightly coat each potato with olive oil, using a pastry brush.
Cook and Baste The Hasselbacks: Bake for 35 minutes. Heat the chive butter in the saucepan just until it melts. Baste the top of each potato with about 1 teaspoon of melted butter, letting it drip into the slits. Bake for another 30-40 minutes longer, or until the potatoes are nicely browned in spots and cooked through.
To Serve: Serve hot. Just before serving top each potato with a teaspoon or two of compound butter. Season potatoes with sea salt and cracked pepper, to taste. Sprinkle generously with remaining chopped chives.