[For crust]: Position rack in center of oven; preheat to 375°F. Butter 9-inch tart pan with removable bottom. Blend flour, sugar, and salt in processor. Add 1/2 cup butter; process until mixture resembles coarse meal. Add egg yolks; process until moist clumps form. Add cocoa nibs; blend in using on/off turns.
Press dough onto bottom and up sides of prepared pan. Bake until crust is golden brown, about 20 minutes. Cool in pan on rack while preparing caramel filling.
[For caramel filling]: Combine sugar and 1/4 cup water in heavy medium saucepan. Stir over medium-low heat until sugar dissolves. Increase heat to high and boil without stirring until mixture is deep amber, occasionally brushing down sides of pan with wet pastry brush and swirling pan, about 7 minutes. Remove from heat; add cream (mixture will bubble vigorously).
Add butter and stir over low heat until caramel is completely smooth. Scrape in seeds from vanilla bean; stir in salt. Cool 10 minutes. Pour warm caramel into crust. Let stand at room temperature until completely cool, about 45 minutes.
[For ganache]: Bring cream to simmer in small saucepan. Remove from heat; add chocolate. Whisk until smooth. Let stand until slightly cooled but still pourable, about 10 minutes.
Pour ganache evenly over caramel filling. Refrigerate tart uncovered until chocolate is firm, about 2 hours. do ahead Can be made 2 days ahead. Cover and refrigerate.
Brush top of tart with gold dust, if desired. Cut tart into thin slices. Arrange 1 slice on each plate. Spoon berries and crème fraîche alongside.