Preheat oil in a fryer, dutch oven, or a medium sauce pot to 340-350°F. (If using a pot on a stove top, I recommend a medium setting.)
Open the can of refrigerated biscuits and carefully take them apart. Let biscuits rest on the board for a few minutes, while the oil is warming up.
Fry biscuits, 2-3 at a time, until golden brown. Flip to the other side and fry until that side is golden brown as well.
Place some paper towels on a wire rack. Take out cooked doughnuts and place them on the wire rack to cool.
Beat cream cheese, sugar, sour cream and Bailey's Irish Cream in a bowl for 2-3 minutes. Transfer cheesecake mixture into a piping bag fitted with a pastry filling tip. Set aside.
Once doughnuts are cool for a couple of minutes, fill each doughnut with some cheesecake mixture from the piping bag.
Chop milk chocolate and place it in a small mixing bowl.
Bring Bailey's to simmer, be careful not to let it actually boil. Pour hot cream over the chopped milk chocolate and stir with a whisk until melted and smooth.
You can dip each doughnut into the chocolate ganache or spoon ganache over each doughnut.