1. Preheat oven to 450°.
2. Combine vinegar and garlic in a small bowl; let stand 5 minutes. Stir in mayonnaise, mustard, and parsley.
3. Cut potatoes lengthwise into 1/4-inch-thick slices; stack slices and cut lengthwise into 1/4-inch-thick strips. Place in a large bowl; cover with hot water. Let stand 10 minutes. Drain potatoes; pat dry with paper towels. Combine potatoes, oil, and salt in a large bowl; toss gently to coat. Arrange potatoes in a single layer on a baking sheet coated with cooking spray. Bake at 450° for 35 minutes; carefully turn over and bake an additional 10 minutes or until lightly browned. Serve with sauce.