In a large mixing bowl, combine pumpkin, brown sugar, cinnamon, ginger, nutmeg, and salt. Whisk eggs then add to pumpkin mixture along with milk and rum. Mix well. Pour into prepared pie shell. Sprinkle the chopped walnuts all around the edge of the pie. Bake at 375-degrees on the lower oven rack for 50-55 minutes (until a toothpick inserted in the center comes out clean).