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1
Roll out Pate Sucree disk on a lightly floured work surface to a 1/8-inch-thick round, dusting with flour as necessary to prevent sticking. Transfer crust to tart pan; press onto bottom and up sides of pan. Trim dough flush with edge of pan. Chill for 1 hour.
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2
Meanwhile, preheat oven to 350u00b0. Spread out chopped pecans in a single layer on a rimmed baking sheet and toast, stirring once or twice, until lightly browned and aromatic, 8-10 minutes.
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3
Place butter in a small skillet over medium heat. Scrape in seeds from vanilla bean; add bean. Cook, swirling pan a few times, until butter browns and smells nutty, about 5 minutes. Discard vanilla bean.
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4
Whisk sugar, both corn syrups, and salt in a large bowl. Whisk in warm brown butter, then eggs; whisk to blend. Spread chopped pecans in an even layer over prepared tart shell. Scatter chocolate over. Place pecan halves in concentric circles over chopped pecans and chocolate. Pour filling slowly and evenly over nuts.
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5
Bake tart until filling is just set in center, 45-50 minutes.
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6
Transfer tart to a wire rack; let cool for at least 30 minutes. DO AHEAD Tart can be made 8 hours ahead. Let stand at room temperature.
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7
Beat cream, creme fraiche, and bourbon until soft peaks form. DO AHEAD Bourbon whipped creme fraiche can be made 4 hours ahead. Cover; chill. Rewhisk before serving.
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8
Remove pan sides. Cut tart into wedges. Serve warm or at room temperature with bourbon whipped creme fraiche.
