Cut the pork into 4-inch chunks and season all over with the 1 tablespoon of the kosher salt.
Put the pork on a rimmed baking sheet and put in the oven. Roast for 20 minutes to sear and render some of the fat. Remove from the oven and reduce temperature to 325 (160C) degrees.
Heat the olive oil in a large Dutch oven over medium-high heat. Add the onion and leeks and cook until softened and lightly golden.
Pour in the wine and let it bubble for 1 minute. Add the remaining ingredients plus 1 -1/2 teaspoons salt and stir. Nestle the reserved pork into the pot and cover the pan.
Place the pot in the oven and cook 3-3 1/2 hours. The meat should be very tender when prodded with a fork.
Serve the pork and beans over cooked pasta or with warm crusty bread.
To make this recipe in your electric slow cooker: Sweat the leeks and onions until softened, and then sear the pork in a stovetop-safe insert or in a large skillet. Another option is to sear the pork in the oven as in the recipe before adding all the remaining ingredients to the slow cooker. Cook on low for 6- 8 hours.
Serve over pasta or with crusty bread and a salad.