1. Trim stems off figs. Cut figs into 1/8-in.-thick slices and put in a large bowl. Bring 6 cups of water to a boil and pour over figs. Let sit 10 minutes. Drain and put figs in a large pot over medium-high heat with wine, 1 cup sugar, and 1/2 tsp. salt. Bring to a boil. Meanwhile, tie up peppercorns, cinnamon, allspice, and cloves in a 6- by 6-in. piece of cheesecloth and add to pot. Lower heat to maintain a simmer and cook until figs are soft and liquid is reduced to about 3/4 cup, about 2 hours. Remove spices and discard. Stir in vanilla. Let figs and liquid cool to room temperature.
2. Meanwhile, in a large bowl, stir together flour, remaining 3 tbsp. sugar, and remaining 1/4 tsp. salt. Drop in butter and work it into the flour mixture with your fingertips, a pastry blender, or a fork until it resembles coarse cornmeal with some pea-size chunks. Quickly stir in 2 tbsp. very cold water until dough starts to hold together (it will still be quite crumbly). Gently knead dough 2 or 3 times in bowl, then turn onto a large piece of plastic wrap, shape into a 6-in. disk, cover with wrap, and chill for at least 1 hour and up to 3 days.
3. Preheat oven to 350°. Place a 10-in. tart pan with a removable rim on a large baking sheet. Butter a large piece of foil. Unwrap dough and put on a floured surface. Roll dough into a 13-in. circle, turning 90° between each pass of the rolling pin to keep it from sticking. Transfer to the tart pan, allowing the dough to fall into place (if you push or stretch it, it will shrink back when baked). Trim edges 1/2 in. past rim of pan and fold down to double the thickness of the tart edge. Set foil, buttered side down, gently onto dough and top evenly with pie weights, dried beans, or rice. Bake 30 minutes. Remove weights and foil and bake until golden brown, about 15 minutes. Let cool.
4. Arrange cooled figs in cooled crust and pour fig-cooking liquid over them. Let sit at least 1 hour (at room temperature) and up to overnight (in refrigerator). Serve at room temperature, with crème fraîche.
Note: Nutritional analysis is per serving.