Position a rack in the center of the oven and preheat to 400 degrees . In a medium bowl, whisk together the 1 tablespoon melted butter, the sugar, egg white and 1 pinch salt; fold in the walnuts. Spread the walnut mixture in an even layer on a rimmed baking sheet and bake until golden-brown, 6 to 8 minutes. Using a metal spatula, loosen the nuts from the pan and transfer to a cutting board. Let cool, then coarsely chop.
In a large Dutch oven, melt the remaining 4 tablespoons butter over medium-low heat; add the onions and cook, stirring occasionally, until softened but not browned, about 10 minutes. Stir in the chicken broth and port, cover partially and simmer for 10 minutes. Stir in the chestnuts and cook for 5 minutes. Gradually whisk in the chestnut puree and cook until heated through, about 5 minutes more. Using an immersion blender, puree the soup (or mix in batches using a standing blender). Season with salt and pepper.
Ladle the soup into 10 bowls. Swirl 1 tablespoon cream into each serving. Sprinkle the parsley and candied walnuts on top.