In a bowl, dissolve yeast in warm water. In a small bowl, combine shortening and boiling water. Stir in milk and extract; cool to 110°-115°. Add to yeast mixture. Beat in eggs, sugar, salt and nutmeg. Add enough flour to form a soft dough. Turn onto a floured surface; knead until smooth and elastic, about 5 minutes. Cover and let rest for 10 minutes.
On a floured surface, roll out dough to an 18x12-in. rectangle. Cut into 6x1-in. strips. Cover and let rise in a warm place until doubled, about 1 hour.
Heat oil in an electric skillet or deep-fat fryer to 375°. Fry dough strips in oil for 2 minutes or until golden brown, turning once. Drain on paper towels.
For frosting, combine brown sugar, butter and cream in a saucepan. Bring to a boil; boil and stir for 2 minutes. Remove from the heat. Stir in confectioners' sugar and vanilla; beat with portable mixture until creamy. Frost the long johns.