Step 1: Make the Dough

1. In a small bowl, mix the warm milk, sugar, and yeast. Let sit for 5 minutes until frothy.
2. In a large bowl, combine flour and salt. Add the yeast mixture, melted butter, egg, and vanilla extract. Mix until a dough forms.
3. Knead for about 8 minutes until smooth and elastic.
4. Place the dough in a greased bowl, cover, and let it rise for 1 hour or until doubled in size.

Step 2: Shape and Fry the Donuts

5. Roll out the dough to ½-inch thickness and cut into rounds (about 3 inches wide).
6. Place the cut dough on a lined baking sheet, cover, and let them rest for 30 minutes.
7. Heat vegetable oil in a deep pan to 350°F (175°C). Fry the donuts for about 2 minutes per side until golden brown. Drain on a wire rack.

Step 3: Prepare the Vanilla Bean Custard

8. In a saucepan, heat milk and heavy cream with the vanilla bean. Simmer, then remove from heat.
9. In a bowl, whisk egg yolks, sugar, and cornstarch. Slowly whisk in the warm milk mixture.
10. Return to heat, stirring constantly until thickened. Remove from heat and stir in butter.
11. Let the custard cool, then transfer to a piping bag.

Step 4: Fill and Brûlée the Donuts

12. Poke a hole in each donut and fill with vanilla custard.
13. Sprinkle the tops with granulated sugar and caramelize with a kitchen torch until golden and crisp.