Prepare the Donut Batter: Preheat the oven to 350°F. Lightly grease a 12-cavity donut pan. In a large bowl, whisk together the flour, granulated sugar, baking powder, and salt. In another bowl, whisk the eggs, whole milk, melted butter, and vanilla extract. Add the wet ingredients to the dry ingredients and mix just until combined. Avoid overmixing.
Fill the Donut Pan: Transfer the batter to a piping bag or resealable bag with the corner snipped off. Pipe the batter evenly into the prepared donut cavities, filling each cavity about three-quarters full.
Bake Until Lightly Golden: Bake for about 15–18 minutes, or until the donuts are lightly golden and a toothpick inserted into the thickest part comes out clean. Let them cool in the pan for a few minutes, then transfer them to a wire rack to cool completely.
Make the Vanilla Custard: In a saucepan, whisk together the egg yolks, granulated sugar, and cornstarch until smooth. Gradually whisk in the heavy cream. Cook over medium-low heat, stirring constantly, until the mixture thickens into a smooth custard. Remove from the heat and stir in the vanilla extract. Transfer to a bowl, cover the surface, and cool completely.
Fill the Donuts: Transfer the cooled vanilla custard to a piping bag fitted with a small round tip. Make a small opening in the side or bottom of each cooled donut and gently pipe the custard inside. Avoid overfilling.
Add the Sugar Topping: Sprinkle a thin, even layer of granulated sugar over the top of each filled donut. Make sure the sugar is distributed evenly for the best caramelized finish.
Caramelize the Sugar: Using a kitchen torch, carefully caramelize the sugar until it melts and turns golden brown. Keep the torch moving continuously to prevent the sugar from burning. Let the caramelized topping cool briefly until crisp.
Serve and Enjoy: Serve the Baked Crème Brûlée Donuts once the caramel topping has hardened. Enjoy them with coffee, tea, fresh berries, or your favorite brunch drink.