Step 1

Heat the oven to 325°F with a rack in the lower-middle position. Mist a 9-inch tart pan with removable bottom with cooking spray. Line a rimmed baking sheet with kitchen parchment.

Step 2

To make the tart shell, in a food processor, process until combined both flours, the sugar and salt, about 5 seconds. Scatter the butter over the mixture and pulse until it resembles coarse sand, 10 to 12 pulses. Add the egg yolk and vanilla, then process until the mixture is evenly moistened and cohesive, 20 to 30 seconds; the mixture may not form a single mass.

Step 3

Crumble the dough into the prepared tart pan, evenly covering the surface. Using the bottom of a dry measuring cup, press into an even layer over the bottom and up the sides; the edge of the dough should be flush with the rim. Use a fork to prick all over the bottom, then freeze until the dough is firm, 15 to 30 minutes.

Step 4

While the dough chills, to make the filling, pour ¼ cup water into a medium saucepan. Add the sugar and honey into the center, avoiding contact with the sides. Cook over medium, swirling the pan frequently, until the mixture is amber in color, about 8 minutes. Off heat, add the crème fraîche, butter, vinegar and salt, then whisk until the butter is melted and the mixture is well combined. Let cool until just warm, about 30 minutes.

Step 5

While the caramel cools, set the dough-lined tart pan on the prepared baking sheet. Bake until lightly browned, about 30 minutes. Cool on the baking sheet on a wire rack for about 5 minutes.

Step 6

Whisk the yolks into the warm honey filling, then add the nuts and stir until evenly coated. Pour the filling into warm tart shell, then gently spread in an even layer. Bake until the edges of the filling begin to puff and the center jiggles only slightly when gently shaken, 25 to 35 minutes.

Step 7

Let the tart cool on the baking sheet on a wire rack for about 1 hour. Remove the pan sides. Serve warm or at room temperature.