Make the tangzhong by stirring the flour and milk in a nonstick pan over medium heat until they form a thick paste.

Mix the tangzhong with cold milk and yeast in the bowl of your standing mixer and let sit for 5 minutes.

Add all the other ingredients for the dough, leaving out half of the butter. Knead at medium-high speed using a dough hook for 5 minutes until the dough starts to come together.

Add the remaining butter and knead again for 5-8 minutes until a smooth and stretchy dough has formed.

Cover and let the dough rise for about 1 hour until it doubles in size.

Roll the dough into a ? inch thick sheet. Cut out 4" circles.

Place the circles onto small pieces of parchment paper and transfer them to a tray. Rest for about 30-45 minutes at room temperature.

Heat 2-3 inches of oil in a wok over medium heat to 350?F. Carefully drop in a test donut and fry for about 2 minutes per side. Fry all donuts.

Let the donuts cool down on a wire rack at room temperature.

For the creme patisserie, whisk the eggs, corn starch, salt, and sugar in a bowl.

Place the milk and vanilla in a nonstick pan and bring to a boil.

Carefully pour the milk mix into the egg mix while whisking continuously, then pour back into the pan.

Cook on low heat while stirring constantly until custard-like consistency. Add the butter and mix it in.

Remove from heat and strain to ensure smoothness. Place in the fridge for at least 15 minutes to cool.

Transfer the creme patisserie into a piping bag. Carefully puncture the donuts and fill them with custard until heavy.

For the caramel, mix sugar, salt, and water in a nonstick pan on low heat.

Once caramel reaches a deep golden color, take it off the heat.

While the caramel is still hot, dip your donuts on one side for a thin caramel coating. Reheat the caramel if it hardens.

Let the donuts cool to form a crispy coating.