Make crust: Fit dough into bottom and up sides of 9-inch tart pan with removable bottom; trim and reroll excess and refrigerate until ready to use.
Heat oven to 375°F. Press large piece of parchment paper into tart shell and fill with pie weights. Bake 15 minutes. Remove parchment and weights and bake until pastry feels sandy and just starts to turn golden, 10 to 15 minutes. Transfer to wire rack and lower oven temperature to 350°F.
Make filling: In medium saucepan, bring cranberries, sugar, lime zest and juice, and 1⁄4 cup water to a boil on medium-high. Lower heat and simmer until berries start to burst, 8 to 10 minutes (a few more minutes for frozen berries).
Strain mixture through large sieve into clean medium saucepan and press through gently, scraping underside into pan. Stir in butter to melt, then eggs, yolks, and salt. Cook on low, stirring constantly, until curd thickens slightly, 8 to 10 minutes (do not boil).
Pour filling into prepared crust and bake until mostly set but still jiggles, 10 to 15 minutes. Transfer to wire rack, let cool to room temperature, then refrigerate at least 2 hours, up to overnight.
Make pie leaves: Using leaf-shape cutter, cut out leaves from remaining dough and place on parchment. Use skewer to etch leaf veins and freeze 10 minutes. Slide parchment onto baking sheet, lightly brush with egg, and sprinkle with sugar. Bake, rotating pan halfway through, until golden brown, 10 to 15 minutes. Let cool.
Make sugared cranberries: Line rimmed baking sheet with parchment paper. In small saucepan, bring 1/4 cup sugar and 1⁄2 cup water to a boil, swirling pan to melt sugar. Boil 1 minute, then remove from heat. Add cranberries, toss to coat, and strain over bowl. Working in batches, toss berries in 1/3 cup sugar. Transfer to prepared baking sheet and let cool and dry, at least 20 minutes. (Leftover syrup can be used in drinks.)
Make sugary pecans: Heat oven to 300°F. Line rimmed baking sheet with parchment. In small bowl, whisk egg white with 1 tsp water until very frothy; transfer 11/2 teaspoons to medium bowl and toss with pecans to coat. Add sugar and salt and toss again. Arrange in single layer on prepared baking sheet and bake, stirring halfway through, until coating is dry and pecans are toasted, 10 to 15 minutes. Let cool.
To decorate: Pipe or spoon whipped cream onto tart, then top with pie leaves, sugared cranberries, and sugary pecans.