Heat 2 cups of milk in a saucepan over medium heat until it bubbles. In a bowl, whisk 4 egg yolks, 1/4 cup of cornstarch, and 1/2 cup of sugar until smooth. Gradually pour hot milk into egg mixture while whisking. Return mixture to saucepan and cook over medium heat until thickened, about 5 minutes. Remove from heat, stir in 2 tablespoons of butter and 1 teaspoon of vanilla extract. Chill in refrigerator until ready to use.

In a mixing bowl, combine 3/4 cup of warm milk, 1 packet of instant yeast, and 1/4 cup of sugar. Let sit for about 5 minutes until bubbly. Add 3 cups of all-purpose flour, 1/2 teaspoon of salt, and 2 melted tablespoons of butter. Stir until a soft dough forms. Knead on a floured surface for about 8 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise in a warm place until doubled, about 1 to 1.5 hours.

Once the dough has risen, punch it down and roll out to about 1/2 inch thick on a floured surface. Cut out circles with a donut cutter. If you don't have one, use a large glass and a smaller one for the center. Place on a baking sheet lined with parchment paper. Cover with a kitchen towel and let rise in a warm area for about 30 to 60 minutes until puffed up.

Preheat oven to 375°F (190°C). Bake donuts for about 10 minutes until golden brown and spring back when lightly pressed. Remove and let cool completely on a wire rack.

Once cooled, create a small hole in the side of each donut with a knife or filling tool. Fill a piping bag with the chilled pastry cream. Gently insert the tip into the hole, squeezing until donuts feel slightly heavy.

In a skillet over medium heat, add 1 cup of granulated sugar. Stir constantly until it melts and turns a deep amber color, about 5-7 minutes. Remove from heat and let cool slightly. Dip the tops of each filled donut into the melted sugar, allowing excess to drip off. Let sit on a cooling rack until sugar hardens.