In a small bowl, combine ¼ cup warm water, yeast, and 1 teaspoon sugar. Let stand until foamy, about 5 minutes.
In a large bowl, beat remaining 3 tablespoons sugar, shortening, and salt at medium speed with a mixer until smooth. Add ½ cup boiling water and evaporated milk, beating until combined. Add egg, beating until smooth. Stir in yeast mixture.
Gradually add 3 cups fl our, beating until smooth. Beat in enough remaining flour to make a soft dough.
On a lightly floured surface, turn out dough, and knead 6 to 8 minutes or until dough is smooth and elastic. Place dough in a lightly greased bowl, turning to grease top. Cover and refrigerate for at least 30 minutes or up to 2 hours.
On a lightly floured surface, roll out dough to ¼-inch thickness. Using a sharp knife, cut dough into 12 (3-inch) squares. Do not reroll dough.
In a large Dutch oven, pour oil to a depth of 3 inches; heat to 350° over medium heat. Fry dough in batches for 2 to 3 minutes or until golden brown, turning dough frequently during frying. Drain on paper towels. Sift confectioners’ sugar over hot beignets. Serve warm with Caramel Sauce and chopped pecans, if desired.
MAKES ABOUT 1 1/2 CUPS
1/2 cup brown sugar
2 tablespoons water
1 tablespoon corn syrup
1 teaspoon vanilla
3/4 cup evaporated milk
In a small saucepan, whisk together sugar, water, corn syrup, and vanilla over medium-high heat.
Cook, stirring occasionally, for 8 minutes or until temperature registers 260º on a candy thermometer.