Step 1Sort the beans to remove any dirt or stones. Rinse and place them in a small saucepan with enough water to cover by 4 inches. Bring the beans to a rolling boil over high heat for 5 minutes. Remove from the heat, cover the pot and let stand for 2 hours.
Step 2While the beans cook, cut the squash in half lengthwise and scrape out the seeds. Cut the flesh into cubes -- the optimum size is three-quarters of an inch, but the skinnier parts of the squash will yield smaller pieces. Set aside.
Step 3Strain the beans through a colander and rinse well. Wipe the pot clean and return the beans to it along with 4 cups of water. Add 1 teaspoon sea salt and bring to a rolling boil. Lower the heat, cover the pot and cook, stirring occasionally, for 45 minutes, or until the beans are soft but not falling apart. (The older the beans, the longer they will take to reach this state.) Drain and set them aside.
Step 4In a large, deep skillet or Dutch oven, heat 2 tablespoons of the butter over medium heat. Add the leeks and season with a good pinch of sea salt. Cook, stirring frequently, for 5 minutes, or until the leeks are softened. Raise the heat to medium-high, add the remaining butter and, when it melts, add the mushrooms, squash and 2 tablespoons of the sage. Season with 1 teaspoon of the salt and 1 teaspoon pepper and cook, stirring often, for 5 to 10 minutes, until the squash begins to brown. Add the cognac, scraping and stirring to loosen the crust on the bottom of the pan. Add the vegetable stock or water and the beans and mix well. Reduce the heat to low and cook, covered partway, for 10 to 15 minutes, until the vegetables and the largest chunks of squash are soft (the smaller ones will mostly "melt").
Step 5Stir in the cream and the remaining 1 tablespoon sage and heat through. Taste and adjust the seasoning before serving.