Prepare the Dough
In the bowl of a stand mixer, combine flour, yeast, sugar, eggs, butter, milk, liqueur, and salt.
Knead on low to medium speed for about 12 minutes until smooth, soft, and slightly sticky.
Cover and let rise for 1 hour or until doubled in size.
Make the Vanilla Cream
In a bowl, whisk egg yolks, cornstarch, sugar, vanilla, and salt.
Heat milk in a saucepan until hot but not boiling.
Slowly whisk hot milk into the yolk mixture.
Return mixture to the saucepan and cook over medium heat, stirring constantly until thickened.
Remove from heat and stir in white chocolate and butter until smooth.
Cover with plastic wrap directly on the surface and chill completely.
Shape and Fry
Divide dough into 45 to 50 gram portions and shape into balls.
Place each on parchment paper squares and let rise for 1½ hours until doubled.
Heat oil to 320°F to 340°F.
Fry donuts for about 3 minutes per side until golden brown. Cool completely.
Fill and Finish
Transfer chilled cream to a piping bag fitted with a small tip. Fill each donut with cream.
In a saucepan, heat sugar and water over medium heat until a golden caramel forms.
Carefully dip the tops of the filled donuts into the caramel. Let excess drip off and cool until set.