How to Make It
Make the pastry In a food processor, pulse the flour with the confectioners’ sugar, baking powder and fine sea salt. Add the butter and pulse until the mixture resembles coarse meal. Add the egg yolks and 1 tablespoon of ice water and pulse until the pastry just comes together; add another tablespoon of ice water if it seems dry. Turn the pastry out onto a work surface and pat into a disk. Wrap in plastic and refrigerate until chilled, 1 hour.
On a floured work surface, roll out the pastry to a 12-inch round. Ease the round into a 10-inch fluted tart pan with a removable bottom, pressing it into the corners and up the side, patching any tears. Trim off any overhang. Freeze the tart shell for 30 minutes.
Preheat the oven to 375°. Line the tart shell with parchment paper and fill it with pie weights or dried beans. Bake in the center of the oven for 20 minutes. Remove the parchment and weights. Bake the shell for 10 to 15 minutes longer, until lightly browned. Let cool completely. Leave the oven on.
Meanwhile, make the filling In a small saucepan, melt the butter over moderate heat. Remove from the heat, add the rosemary and let steep for 20 minutes. Strain the butter into a small bowl and let cool.
Spread the hazelnuts on a rimmed baking sheet and toast in the oven until fragrant and golden and the skins are splitting, about 12 minutes. Let cool slightly, then transfer to a kitchen towel and rub together to remove the skins; let cool. Coarsely chop the hazelnuts and spread them in the cooled tart shell. Put the tart shell on a rimmed baking sheet. Reduce the oven temperature to 300°.
In a large bowl, beat the whole eggs and yolks with the brown sugar, brown rice syrup, honey and fine sea salt. Gradually whisk in the rosemary butter, then whisk in the cream, flour and vanilla. Pour the filling into the tart shell and sprinkle flaky sea salt on top. Bake the tart for 50 minutes, until the filling is set at the edge but slightly jiggly in the center. Let cool completely. Serve at room temperature or slightly chilled, topped with a dollop of whipped crème fraîche alongside.