In bowl of stand mixer fitted with whisk beater, place butter and powdered sugar. Beat on low speed until well mixed. Increase speed to high; beat about 4 minutes or until soft and fluffy.
Scrape down bowl. Add milk and vanilla; beat 4 minutes longer. Set aside.
Pour canola oil into 10-inch-wide saucepan or Dutch oven until at least 2 1/2 inches deep. Heat oil over medium heat until deep-fry temperature reads 375°F. Line large plate with paper towel; set aside.
Separate dough into 8 biscuits. Place 4 biscuits in hot oil; fry 2 minutes 30 seconds. Using spatula, flip biscuits over; fry 2 minutes 30 seconds longer. Transfer doughnuts to paper towel-lined plate to absorb any oil. Toss doughnuts in granulated sugar.
Using handle of wooden spoon, poke a hole in side of each doughnut. Fill decorating bag fit with small hole tip with Vanilla Cream. Squeeze enough vanilla cream into each doughnut to fill hole.