Melt butter in a medium, heavy-bottomed saucepan over medium heat. Add sugar and whisk until sugar melts and mixture begins to boil, about 5 minutes. Stir in milk, vanilla, and pecans until smooth. Set aside.
In heavy-bottomed skillet, melt the shortening over medium heat until it reaches 325 degrees F. Use a meat or candy thermometer for this – you don’t want to let the oil get over 350 degrees or it will start to smoke. If you see it smoking, remove it from the heat to cool down until you are ready.
Separate biscuits and cut into fourths. Fry biscuit quarters in batches until golden on each side. Biscuits will cook very quickly.
Dust generously with powdered sugar and serve immediately with praline sauce.