1. Place flour in a large bowl. Cut shortening into flour with a pastry blender or fork until crumbly. Combine hot water and sugar in a small bowl, stirring until sugar dissolves. Let cool to room temperature; add vanilla, if desired. Add sugar mixture to flour mixture, stirring with a fork just until dry ingredients are moistened. (Dough will be sticky.)
2. Pour oil to depth of 3 inches in a Dutch oven; heat to 375°.
3. Meanwhile, turn dough out onto a well floured surface, and knead lightly 3 or 4 times. Roll dough to 1/4-inch thickness; cut into 2-inch squares, and place on wax paper-lined baking sheets. Let dough rest 10 minutes.
4. Fry beignets, in batches, 1 minute on each side or until golden brown. Drain on paper towels, and dust generously with powdered sugar. Serve hot.