Make the tart shell. In a food processor fitted with the blade attachment, beat the butter and sugar until creamy and totally smooth. Add the egg yolk, vanilla, salt, espresso powder and cocoa powder, and mix on low just until it all comes together. You will need to scrape down the bowl a few times.

Dump in the flour and pulse just until the dough comes together and starts to ball up in the mixer. You can also make this dough with softened butter in a stand mixer fitted with the paddle attachment; just follow the same instructions.

Scrape out the dough onto a sheet of parchment or a silicone mat. Cover with another sheet of parchment or silicone mat (or even plastic wrap) and roll it out to a big circle with about a 1/6-inch thickness. When you place your tart pan in the center of the dough, you should have about a 1.5-inch border all the way around. Chill the dough in the refrigerator until firm.

Preheat the oven to 350°F and set a rack to the middle position. Remove the top layer of parchment (or silicone or plastic wrap) from the dough and invert it onto a 9 or 10-inch round tart tin. Peel off the remaining parchment and gently encourage the dough to sink down into the pan. You may have to be patient and let it warm up a bit so it doesn’t crack. Press the dough into the pan and run a sharp knife around the edges to cut off any excess (which you can use to patch any cracks or holes.)

Chill the tart in the freezer until very firm, about 10 minutes. Crumple up one of the parchment sheets and place it in the tart shell. Fill it with pie weights (dried beans or sugar also work well). Bake for 9 minutes, then lift the weights out of the shell, dock holes in the shell all over with a fork, and continue baking for 6 minutes or until it looks dry and totally set. Cool on a wire rack.

Make the caramel. Scrape out the seeds from the vanilla bean and add them plus the pod to a small saucepan with the heavy cream and coffee beans. Heat on the stove over medium-low just until the mixture is barely simmering, then turn the heat off and cover.

Heat the water, sugar and corn syrup in a medium saucepan over medium-low heat. Stir just until combined. While that cooks, strain the heavy cream mixture, measure out 1/3 cup (79 milliliters) and set aside the rest. Keep that and the butter nearby.

Once the sugar mixture turns a deep amber color and you begin to see wisps of smoke, remove from the heat.

Pour the 1/3 cup of coffee-infused heavy cream into the caramel, then the butter, stirring vigorously until it comes together. Stir in the salt and vanilla extract (if not using a bean).

Return the caramel to the stovetop and cook on medium-low until a candy or instant-read thermometer reads 240°F. Immediately remove from the heat and pour into the baked tart shell.

Before serving, allow the tart to warm up a bit at room temperature for 15 minutes. Heating up a sharp knife over a stove burner or in some hot water will make slicing super easy.