To make the beans, cover them with cold water and soak for at least 7 hours. Drain the beans, then rinse and put them in a medium saucepan. Cover them with at least an inch of water and add a teaspoon of salt, the peppercorns, olive oil, thyme and garlic. Bring to a boil, give them a stir and lower the heat so the beans are gently simmering. Cook until just tender, 30 to 40 minutes. Drain the beans, removing the garlic, peppercorns and thyme, and set aside.
To make the stew, heat the oven to 350° F. Put 1 tablespoon of the olive oil in a medium Dutch oven and set over medium-high heat. When the oil just starts to smoke, season half the pork well with salt and add it to the pot. Brown the cubes on all sides, about 5 minutes total. Remove the pork to a plate with a slotted spoon and repeat with the rest of the meat, adding more oil if necessary.
When the pork is browned, turn the heat to low and add the onion and a pinch of salt. Cook, stirring frequently, until softened, about 5 minutes. Add the garlic and cook for another minute, until fragrant. Stir in the mustard, tomato paste and paprika and cook for another 2 minutes.
Add the tomatoes, stock, thyme and 1 teaspoon of salt, as well as the browned pork and any accumulated juices. Stir well and bring the stew to a boil over medium-high heat. When it is simmering, cover the pot and transfer it to the oven. Cook for an hour and a half.
Add the cooked beans and the butternut squash to the pot, stir them gently through, and return the stew to the oven for another 30 to 45 minutes, until the meat and the squash are fork-tender. Taste and adjust the seasonings if necessary. Serve immediately with rice or couscous, or cool and refrigerate to reheat the next day.