1. Prepare the Donut Dough

• In a stand mixer bowl, combine warm milk, water, and yeast. Let sit for 5 minutes until foamy.

• Add flour, sugar, eggs, and salt. Mix on low speed until combined, then increase to medium-low and knead for 6 minutes until elastic.

• Gradually add softened butter, 1 tbsp at a time, waiting until each piece is fully incorporated before adding the next.

• Transfer dough to a greased bowl, cover, and let rise for 1–2 hours until doubled in size.

2. Make the Vanilla Pastry Cream

• Heat milk, sugar, and salt in a saucepan until steaming (do not boil).

• Whisk egg yolks, cornstarch, and sugar in a bowl until pale. Slowly pour in half the hot milk while whisking to temper.

• Return mixture to the saucepan and cook over medium heat, whisking constantly, until thickened (about 5 minutes).

• Remove from heat, stir in butter and vanilla, then strain into a bowl. Cover with plastic wrap (touching the surface) and refrigerate for 2 hours.

3. Shape and Fry the Donuts

• Roll risen dough to ½-inch thickness and cut into 3-inch rounds. Let proof on parchment paper for 30–45 minutes until puffy.

• Heat oil to 350°F (177°C) in a deep pot. Fry donuts in batches for 1–2 minutes per side until golden. Drain on paper towels.

4. Fill and Caramelize

• Use a chopstick to poke a hole in each donut, then pipe in chilled pastry cream.

• For the caramel, combine sugar and water in a saucepan. Cook over medium heat without stirring until golden amber (8–10 minutes).

• Carefully dip the top of each donut into the caramel, letting excess drip off. Cool on a wire rack until the shell hardens.