In small bowl, dissolve 2 teaspoons (10 mL) of granulated sugar in warm water. Sprinkle in yeast; let stand for 10 minutes or until frothy.
Meanwhile, in bowl of stand mixer fitted with paddle, combine remaining sugar, milk, shortening, eggs and salt. Add yeast mixture and beat at lowest speed until smooth.
Beat in flour, 1/2 cup (125 mL) at a time, scraping bowl as necessary until soft, sticky dough forms.
Transfer dough to lightly greased bowl; cover with plastic wrap. Refrigerate for at least 4 hours or for up to 12 hours.
On lightly floured surface, roll out dough to 1/4-inch (5 mm) thick 20 x16-inch
In deep-fryer or deep saucepan, heat oil to 360°F (185°F) or until 1-inch (2.5 cm) cube of white bread turns golden in 1 minute. Cook beignets, a few at a time to avoid overcrowding and turning frequently, until golden brown, about 2 minutes. Using slotted spoon, transfer to paper towel-lined rack to let cool.
Dust each beignet generously with icing sugar.