In a large pot over high heat, combine the honey, bay leaves, rosemary, thyme, parsley, garlic, peppercorns, kosher salt and water. Cover and bring to a boil, then boil for 1 minute, stirring to dissolve the salt. Remove from the heat and let the brine cool completely. Refrigerate until completely cold before using. The brine can be refrigerated for up to 3 days. This amount is enough for up to 4 pounds of pork. 

Pour the brine into a container large enough to hold the pork belly and add the pork. Refrigerate for 10 hours.

Remove the pork belly from the brine and rinse under cold water. Pat dry with paper towels or let air-dry.

Preheat the oven to 200°F.

Choose a lidded ovenproof pot, such as a 12-quart Dutch oven, that is only slightly larger than the pork belly; it should be large enough that the pork will be surrounded by the lard. Put the belly in the pot and cover with the lard; it should cover the pork by 1/2 to 3/4 inch.

Set the pot over low heat and heat until the lard registers 190°F. Cover, transfer to the oven and cook until the pork is tender, 5 1/2 to 6 hours, but start checking after 4 hours. As the pork cooks, it will lose fat and shrink; it is best to transfer the meat and fat to a smaller pot, always keeping the pork covered by the lard.

Remove the pot from the oven and let the pork cool to room temperature. The pork can simply be refrigerated in its fat, but we prefer to press it, which yields a better texture and appearance. To press it, transfer the pork to a deep baking dish. Pour in enough fat to just cover the pork. Cover with plastic wrap, top with a smaller baking dish, and weight it down with a brick or large can. Refrigerate for at least 12 hours; reserve the extra fat. After being pressed, the pork can be refrigerated, covered by fat, for up to 1 week.

To serve, let the pot sit in a warm spot for 2 to 3 hours to soften the fat. You want to be able to scrape the fat from the pork while keeping the meat as cold as possible for easier slicing. Remove the pork belly from the fat and wipe off any cooking fat that clings to the meat. Remove the skin and score the fat on the pork in a crosshatch pattern. Slice or cut it into squares, and let sit at room temperature for 20 to 30 minutes before sautéing. 

Preheat the oven to 350°F. 

In a large ovenproof frying pan over medium-high heat, warm canola oil just until smoking. Put the pork belly pieces, fat side down, in the pan. Reduce the heat to medium-low and cook until the excess fat is rendered and the fat side is browned, about 18 minutes; pour off excess fat about halfway through the cooking. Transfer the pan to the oven to heat through, about 10 minutes. Remove from the oven and sprinkle with gray salt.

Slice the buns in half, leaving the top half thicker than the bottom. Spread the top bun with mustard. Place the pork belly confit on the bottom bun, cover with the top bun and serve.