Make the yeast mixture: Combine yeast, 1/2 cup warm water, and 1 tsp. granulated sugar in bowl of a heavy-duty stand mixer; let stand 5 minutes. Add milk, eggs, salt, and remaining granulated sugar.
Form a dough: Microwave remaining 1 cup water until hot (about 115°); stir in shortening until melted. Add to yeast mixture. Beat at low speed, gradually adding 4 cups flour, until smooth. Gradually add remaining 2 1/2 to 3 cups flour, beating until a sticky dough forms. Transfer to a lightly greased bowl; turn to grease top. Cover and chill 4 to 24 hours.
Roll and cut: Turn dough out onto a floured surface; roll to 1/4-inch thickness. Cut into 2 1/2-inch squares.
Fry until golden: Pour oil to depth of 2 to 3 inches into a Dutch oven; heat to 360°. Fry dough, in batches, 2 to 3 minutes on each side or until golden brown. Drain on a wire rack. Dust immediately with powdered sugar.
In a saucepan cook the milk and sugars together on medium heat. Stir continuously so sugar does not burn. Cook the mixture until it is at the “soft ball stage.” This requires dropping a tiny drop of the mixture into cold water; the mixture should turn into a ball when it is in the water.
Turn off the heat and add remaining ingredients.
Mix the ingredients until the butter is melted and the pecans are well coated.
Continue to mix until the mixture cools and forms sugar on the side of the pan.
Using a small spoon scoop and drop the mixture onto the greased wax paper.
Let the candy to cool until dry. Candy is dry when it can be taken off wax paper in one piece.