Coarsely grate potatoes, and then spread them out in an even layer on a large tea towel. Roll up tea towel. Squeeze tea towel over sink to remove as much liquid as possible. Transfer grated potatoes into large bowl and season with salt.
Heat oil in large skillet on medium-high heat. Shape grated potato into four balls. Place potato balls in skillet. Press them down to flatten. Fry hash browns without touching them for 4 to 5 minutes per side or until golden brown. Transfer to a paper towel-lined plate.
Warm the poutine gravy over low heat in a small saucepan, stirring occasionally so it doesn't stick to the saucepan.
Meanwhile, mix together the ground beef, green onions, and egg in a bowl. Season to taste. Shape beef mixture into four patties. Preheat the barbecue to medium-high. Place patties on oiled barbecue grill. Cook 6 to 8 minutes per side, or until meat is no longer pinkish. For the last few minutes of cooking, place buns on the grill and toast for 2 minutes, or until golden.
Place a meat patty, a hash brown, cheese curds, poutine gravy, and chives onto each bun.