Bring 6 quarts water to boil and add 2 tablespoons salt.
In a large mixing bowl, mash goat cheese until soft. Add scallions, eggs, nutmeg and cheese and stir well. Using a pasta roller, roll out pasta to thinnest setting and then cut sheets into 2-inch squares. Bring chicken stock to simmer in a 4-quart saucepan. Place 1 teaspoon goat cheese filling in the center of each 2-inch square. Fold opposite corners together to form a triangle. Press edges together firmly to seal. Bring opposite points of the triangle together and meld together with firm finger pressure. Continue until all pasta is done. Drop tortellini in boiling water and cook until tender, about 7 to 10 minutes. Drain well and drop into simmering chicken broth. Add remaining scallions and cheese, check for seasoning and serve immediately.