1. In a medium pot, bring 4 cups water to a boil. Add the raisins, reduce the heat, and simmer for 5 minutes. Drain. Transfer the raisins to a small bowl and cover with the cognac. Cover the bowl tightly with plastic wrap and let sit at room temperature for 1 hour, or refrigerate overnight, or for up to 5 days.

2. Mix together the hazelnuts, bread crumbs, 3 tablespoons of the butter, chopped thyme, and lemon zest, and salt and pepper to taste. Divide the mixture in half and roll each half out between two pieces of parchment paper or plastic wrap into a ¼-inch-thick rectangle. Refrigerate until firm, about 2 hours, or up to 3 days.

3. Put a rack in the lower third of the oven and preheat the oven to 325°F.

4. Drain the raisins and reserve the cognac. If there is any excess fat on the pork butt, trim it off and discard. Cut the pork butt in half and season with salt and pepper. In a medium cast-iron pot or Dutch oven over medium-high heat, warm 2 tablespoons of the olive oil and 2 tablespoons of the butter. Add the pork, garlic, shallots, and 2 of the sprigs of thyme and sear the pork until golden brown on all sides, about 10 minutes.

5. Deglaze the pot by adding the reserved cognac and scraping up any browned bits clinging to the bottom of the pot. Bring the cognac to a boil, and let reduce until almost all the liquid in the pot has evaporated. Add the white wine and chicken stock and return to a boil. Transfer the pork to a plate. Strain the contents of the pot through a colander set over a bowl, reserving the liquid and discarding the garlic, shallots, and thyme.

6. Put the pot back on the stove over medium-high heat and melt the remaining 2 tablespoons butter with the remaining 2 tablespoons olive oil. Add the Jerusalem artichokes and onions and cook, stirring, until light golden brown, about 10 minutes. Add the pork back to the pot along with the reserved liquid and remaining 2 sprigs of thyme and bring to a simmer. Add the raisins, cover, and transfer the pot to the oven.

7. Braise for 2 hours, or until the meat is tender. (At this point, the pork can be cooled and refrigerated overnight, if you wish. This cooling will allow any fat in the braising liquid to come to the top for easy removal. The pork can then be reheated in a 325°F oven for about 30 minutes.)

8. Preheat the broiler. Remove the hazelnut crust from the refrigerator. Transfer the pork to a baking sheet and top each pork half with a piece of crust. Broil until the crust is golden brown, about 3 minutes. If the sauce is too thin or is not flavored intensely enough, ladle most of it off into another pot and simmer it until it thickens and intensifies. Then add it back to the original pot. Slice the pork, serving equal pieces of the crust. Spoon the braising liquid over the pork and serve.