Heat oven to 350°F (175°C).

Make the crust: Combine the flour, salt, and sugar in the bowl of a food processor. Add butter and vanilla to the bowl, then run the machine until the mixture forms large clumps. Set a marble or two of dough aside, and transfer the rest of it to a 9-inch round tart pan with a removable bottom set on a large baking sheet. Press the dough evenly across the bottom and up the sides. Transfer to freezer for 15 minutes, until solid.

Parbake crust: Once firm, prick all over with a fork. Coat a piece of foil with nonstick spray, and press it oiled-side-down tightly against the frozen crust. Bake tart with foil for 15 minutes, then carefully peel back foil and discard. If cracks have formed, use the marbles of dough you set aside to patch it. Return to oven for 5 minutes, until just barely golden at edges and dry to the touch. Set aside.

Meanwhile, make filling: In a medium saucepan, melt butter over medium heat and continue cooking it, stirring frequently, until it smells nutty and brown bits form at the bottom of the pot. Whisk in brown sugar and golden syrup or honey and cook at a simmer, whisking constantly, for one minute. Pour into a large bowl, scraping out all of the browned bits from the pot, and place in the fridge for a few minutes, until it has cooled somewhat. Whisk in apple cider vinegar, vanilla, and eggs, one at a time, then stir in peanuts.

Bake tart: Pour filling into prepared tart shell, top with a little flaky salt, and bake for 23 to 28 minutes, until just faintly jiggly in the center and golden brown all over. Cool on a rack to room temperature.

Serve: Decorate with powdered sugar if desired. Serve in wedges at room temperature with a dollop of sour cream.