Prepare the Sugared Cranberries: Stir together water and 1 3/4 cups of the sugar in a medium saucepan. Place over medium, and bring to a simmer, stirring often until sugar dissolves. Continue simmering sugar syrup, without letting it boil, until it thickens slightly, 8 to 10 minutes. Remove from heat, and cool until warm, about 5 minutes. (If cranberries are combined with the sugar syrup when it is too hot, they may burst from the heat.)
Combine fresh cranberries and warm sugar syrup in a large bowl. Cool to room temperature, stirring occasionally. Cover bowl, and chill 8 hours or overnight.
Sprinkle a rimmed baking sheet with 1/2 cup of the sugar. Pour chilled cranberry mixture through a wire-mesh strainer over a bowl. (Reserve cranberry syrup in bowl for another use.) Spread cranberries in a single layer on sugar on baking sheet. Sprinkle with remaining 1/2 cup sugar. Gently shake baking sheet, making sure cranberries are evenly coated with sugar. Let stand, uncovered, until cranberries are dry and crisp, about 2 hours. Shake off any excess sugar on cranberries, and place in an airtight container. Store at room temperature for up to 2 days.
Prepare the Crust: Pulse flour and salt in a food processor until combined, 3 to 4 times. Add cubed butter and shortening, and pulse until mixture resembles small peas, 4 to 5 times. Sprinkle 3 tablespoons ice water over top of mixture. Pulse 4 times. Add up to 1 more tablespoon of water, 1 teaspoon at a time, pulsing after each addition until dough just begins to clump together.
Turn dough out onto a lightly floured work surface; knead until dough comes together, 2 to 3 times. Shape and flatten dough into a disk. Wrap in plastic wrap, and chill 2 hours or up to 2 days.
Preheat oven to 375°F. Unwrap chilled pie dough disk and place on a lightly floured surface. Let stand at room temperature until slightly softened, about 5 minutes. Sprinkle dough with flour, and roll into a 12-inch circle. Carefully fit dough circle into a 9-inch glass pie plate; fold edges under, and crimp. Line pastry with parchment paper, and fill with pie weights or dried beans.
Bake in preheated oven 15 minutes. Transfer crust to a wire rack; remove pie weights and parchment, and let crust cool, about 30 minutes. Increase oven temperature to 400°F.
Prepare the Filling: Whisk together sugar, flour, and salt in a large bowl. Add melted butter to flour mixture, stirring with a fork until mixture is combined and resembles damp sand.
Whisk eggs in a medium bowl until well beaten. Add half-and-half and vanilla, and whisk until well combined. Pour egg mixture over sugar-butter mixture, and whisk to combine into a smooth, thick, creamy yellow filling. Pour into prepared piecrust.
Bake at 400°F for 5 minutes. Reduce oven temperature to 375°F. Bake until edges puff up and center is fairly firm, wiggling only slightly when you gently nudge pie plate, about 35 minutes. Transfer pie to a wire rack, and cool to room temperature, about 2 hours.
Prepare the Whipped Cream: Beat whipped cream with an electric mixer in a large bowl on medium-high speed until soft and lightened in texture, about 2 minutes. Add sugar and vanilla, and beat until smooth, fluffy, and well combined, about 2 minutes. Cover and chill until ready to serve. Top pie with Whipped Cream and Sugared Cranberries.