Bring vinegar to a boil in a small saucepan; reduce heat, and simmer until reduced to 2 tablespoons (about 10 minutes). Place in a medium bowl, and cool completely. Add butter, chopped shallots, thyme, 1/4 teaspoon salt, and black pepper; stir well to combine.
Place potatoes in a saucepan; cover with water. Bring to a boil; reduce heat, and simmer 20 minutes or until tender. Drain. Cut potatoes in half; place in a large bowl. Sprinkle with remaining 1/4 teaspoon salt. Add butter mixture and parsley; toss gently to coat. Serve immediately.