How to Make It
Preheat oven to 350°F.
Bring potato and parsnip slices to a boil in a large Dutch oven filled with water. Reduce heat, and simmer 6 minutes (slices should be slightly undercooked at the center). Reserve 1/2 cup cooking liquid; drain. Arrange potato and parsnip slices in a single layer on a baking sheet; cool.
Heat oil in a medium saucepan over medium-high; stir in flour. Stir in reserved 1/2 cup cooking liquid, half-and-half, 1/2 teaspoon salt, and pepper; bring to a boil. Cook 2 minutes or until slightly thickened. Stir in Gruyère cheese; cook 1 minute. Remove pan from heat. Add potato and parsnip slices, remaining 1 teaspoon salt, and parsley; toss gently to combine. Spoon potato mixture into a 2-quart baking dish coated with cooking spray; sprinkle with Parmigiano-Reggiano cheese. Bake at 350°F for 45 minutes or until golden brown.