Preheat oven to 425ºF and set an oven rack in the center position.
- Make the Vinaigrette: Whisk olive oil, lemon juice, garlic, mustard, salt and pepper in a small bowl. Set aside, keeping the vinaigrette at room temperature.
- Peel and slice the potatoes: Peel the skin off the potatoes with a vegetable peeler, scraping a bit of potato off the bottom to make a flat stable surface, so they don't roll around when you're slicing them and dressing them. Make slices, about 1/4 of an inch apart, along the length of the potato, but stopping the cut about 1/4 of an inch from the bottom so the potato holds together. An easy way to keep from cutting all the way through, is to lay the potatoes lengthwise between two wooden-handled spatulas or two chopsticks. The wood on either side of the potato will keep you from cutting all the way through.
- Place the sliced potatoes on a rimmed baking pan. Give the vinaigrette a whisk and spoon 1 tablespoon over each potato. Roll the potatoes around in the pan to coat them. Bake for 45 minutes.
- Pull the pan out of the oven. Give the dressing a whisk and spoon another tablespoon over each potato, aiming to get it to slip into the slits that have started to open up. Bake for 20-30 minutes more, until the potatoes are nicely browned on the outside.
- Whisk the lemon zest and parsley into the vinaigrette and spoon 1 tablespoon over each potato. Serve and enjoy, passing extra vinaigrette on the side.