Using an electric mixer, beat the butter or shortening and sugar in a large bowl until fluffy. Beat in the egg and the brandy. Beat in the salt. Add the flour and beat until blended. Transfer the dough to a lightly floured work surface and knead until a soft dough forms. Form the dough into a ball. Divide the dough into 4 equal pieces. Shape the dough pieces into balls. Wrap the dough balls with plastic wrap and refrigerate 30 minutes.
Working with 1 dough ball at a time, roll the dough ball into a 12-inch diameter round (the dough should be very thin and almost transparent). Using a fluted pastry cutter, trim the edges to form a square shape. Cut the dough into 1-inch strips. Cut each strip in half crosswise to form 5-inch-long strips. Gently stretch the strip gently so that you have enough dough to tie a bow. Repeat with remaining dough strips. Gather the dough scraps, then reroll and cut them to make additional bowtie pastries.
Line a baking sheet with paper towels. Heat the oil in a large heavy frying pan over medium heat to 375 degrees F. Working in batches, fry the pastries until they puff and become golden, turning once, about 2 minutes total. Using tongs, transfer the pastries to the paper towel-lined baking sheet to drain the excess oil. While still hot, dust the pastries generously with confectioners' sugar and serve.
The pastries can be made 2 days ahead. Store in an airtight container at room temperature.
Recipe courtesy of Giada De Laurentiis