Clear a place of honor on the Thanksgiving table for this creamy and exceptionally comforting casserole.
Preheat oven to 350°.
Heat a skillet over medium-high heat. Add oil to pan. Add leek, thyme, and sage; cook 3 minutes. Add greens; cook 2 minutes. Remove leek mixture from pan; place in a bowl.
Combine 1 cup turnips, 1 cup potatoes, 1 cup water, milk, and garlic in a saucepan; bring to a boil over medium-high heat. Reduce heat to medium-low; simmer 10 minutes. Place milk mixture, flour, salt, and pepper in a blender. Remove center piece of blender lid; secure blender lid on blender. Place a clean towel over opening in lid. Blend until smooth.
Coat a broiler-safe 2-quart oval ceramic baking dish with cooking spray. Arrange half of remaining turnips and half of remaining potatoes in dish; top evenly with leek mixture and 1/4 cup cheese. Top with remaining turnips and remaining potatoes. Pour milk mixture evenly over top. Cover tightly with foil. Bake at 350° for 45 minutes. Uncover; bake at 350° for 20 minutes. Remove dish from oven. Heat broiler to high. Sprinkle gratin with remaining 3/4 cup cheese. Broil 3 minutes.