Preheat oven to 325°F. Grease the removable bottom tart pan thoroughly, line the bottom with a parchment paper cutout and grease that too. Set aside until ready to use.
Add all-purpose flour, wheat flour, sugar, and salt to a food processor and process for few seconds to thoroughly incorporate the ingredients. Add cubed cold butter and process until combined. Add one egg yolk, 1 tablespoon vanilla extract and pulse until it is crumbly but not a rolling dough.
Transfer to the prepared tart pan. Distribute the crumbs evenly in the pan before pressing in an even layer at the bottom. Use a measuring cup to smooth the bottom layer while pushing extra crumbs to form a neat fluted edge. Use two fingers, or finger and thumb to even out the edges into a smooth surface for a clean finish.
Dock the surface thoroughly to prevent the crust from developing air pockets. Cover with a plastic wrap and freeze for 20 minutes.
Meanwhile, add ¼ cup water to a heavy saucepan, also add ½ cup sugar, and ¼ cup honey. Cook on medium heat without stirring until it start to get golden brown. Lift the saucepan and swirl and cook until it is dark brown caramel. Be careful, there is a very fine line between golden brown and charred.
Remove from heat and add heavy cream stirring continuously.
Once the sauce is smooth, add 4 tablespoon cubed butter, 1 tablespoon cider vinegar, ¼ teaspoon salt. Continue to cook stirring. When well combined, let it cool for 30 minutes.
At this point, put the crust in the preheated oven for 20 minute or until it is light brown. Remove and let it cool.
Meanwhile, get back to the caramel, and add 2 egg yolk mixing to thoroughly combine. Add walnuts and make sure all the nuts are well coated with the caramel. Transfer the filling to the crust lined, baked, and cooled tart pan. Smooth it out with the back of spoon or offset spatula.
Bake in preheated 350°F oven for 20 to 30 minutes. Let it set for at least 20 minutes before cutting into it. Have a delicious tea time treat, or a dinner dessert.