Make the dough first as it will take the longest to rise. In a large mixing bowl, whisk together warm milk, instant yeast, sugar, salt, and egg until completely smooth.
Add room temperature butter and all-purpose flour to the mixture. Mix together using a hook attachment and stand mixer or a wooden spoon/rubber spatula. Knead the dough for 2 to 3 minutes, then transfer to an oiled bowl. Cover and place in a warm place to rise for 1 hour 30 minutes to 2 hours.
While the dough rises, make the custard filling.
In a mixing bowl, whisk together cornstarch, sugar, and salt. Add all the egg yolks and beat until the mixture lightens in color. Set aside.
In a pot over medium heat, combine the milk, vanilla extract, and vanilla bean. Heat until the mixture starts to bubble at the edges, but do not boil.
Slowly add the warm milk mixture to the egg yolk mixture, a little at a time, to prevent cooking the egg yolks. Whisk until the mixture is smooth.
Transfer the mixture back to the pot and heat over medium-low heat. Whisk continuously for a few minutes until the mixture starts to thicken. Remove from heat and add the butter. Stir until the butter is melted and fully incorporated.
Transfer the custard to a bowl, cover, and chill in the refrigerator.
Flour a working surface and rolling pin. Roll out the dough to 1/2 inch thick or less. Using a heart cookie cutter, punch out small heart donuts. Repeat with scraps until all dough is used. Place on an oiled baking sheet or parchment paper and cover for 30 minutes.
Heat oil in a pot to a temperature of 325°F to 350°F. Fry donuts in the oil, making sure not to crowd them, until golden brown, flipping over halfway. Drain excess oil on a paper towel or wire rack. Repeat with remaining dough.
Fill a piping bag fitted with a small tip or a ziplock bag with the custard filling. Make a deep hole in one side of each donut and insert the piping bag to fill the donut with the custard.
Make the Crème brûlée topping now.
In a small pan over medium heat, add granulated sugar and water. Let it come to a boil and dissolve the sugar.
Allow the mixture to bubble and swirl occasionally, but do not mix it to avoid sugar crystallization. The color should deepen and turn golden.
Once golden, reduce heat to low to continue caramelizing the sugar until it turns golden brown. Remove from heat.
Quickly dip one side of the filled donuts into the caramelized sugar and lift, letting any excess drip off. Place the donuts on a wire rack. Repeat with the rest of the donuts.
Serve warm and enjoy!
