Heat the oven to 400*F. Slice each squash in half and scoop out the seeds and pulp from the inside. Set the seeds aside for later.
Arrange the squash on a baking tray, skin side down, and drizzle each half with olive oil, a sprinkle of sea salt, and a sprinkle of smoked paprika (the paprika is optional but lends a great flavor). Place in the oven and roast until completely cooked through, 30 minutes to 1 hour, depending on the size of the squash.
Remove the squash from the oven and allow to cool until they can be handled.
While the squash is cooling, rinse the pulp away from the seeds under running water. Pour the wet seeds into a clean dish towel or paper towel and lightly dry, then scatter the seeds evenly around on a baking sheet. Sprinkle with sea salt and smoked paprika, then place in the oven and roast for 10-15 minutes, until they are lightly browned and crispy. Remove from oven, turn off the heat, and set the seeds aside to cool.
When the squash can be handled, use a spoon to scrape out the flesh from the skin. Place the cooked flesh in a large pot and add the buttermilk and stock. Turn the heat to low and begin to blend the soup together using an immersion blender. If you don't have an immersion blender, use your blender or a food processor, working in batches, until the soup is creamy and thick. Add the water, a little at a time, until you reach a desired consistency. You may not need all of the water, or you may wish to add a little more for a thinner soup.
Heat the soup slowly and gently until it is cooked through, stirring often. Season to taste with more salt and freshly cracked pepper, if necessary When ready to serve, add a splash of balsamic vinegar to each serving and top with a small handful of the roasted squash seeds.