Yeast Donut Dough 

1. In the bowl of a stand mixer, whisk together the warmed milk and 1 teaspoon of sugar. Next, whisk in the yeast and cover the bowl with a large plate or clean kitchen towel. Set aside for 8-10 minutes or until the mixture takes on a foamy, bubbly appearance with a fermented aroma.
2. In a medium mixing bowl, whisk together the flour, salt, and remaining sugar. Set aside. Using a stand mixer with the dough hook attached, mix the egg and melted butter into the activated yeast at medium speed to combine.
3. Reduce mixer speed to low and mix all of the dry ingredients into the liquid mixture until a shaggy-looking dough forms. Increase mixer speed to medium and knead dough for 6 minutes. The dough will feel soft and tacky to the touch.
4. If the dough is too soft and difficult to handle, mix in additional flour 1 tablespoon at a time until it is more manageable to work with. For light and airy donuts take care to not add too much flour.
5. Transfer the dough into a large greased mixing bowl and cover with plastic wrap or a clean kitchen towel. Place the bowl in a warm part of the kitchen and allow the dough to rise until it has doubled in size, about 60-90 minutes.
6. Gently deflate the dough with a fisted hand, cover the bowl with plastic wrap or a kitchen towel, and let the dough rest for 5 minutes. Cut a large sheet of parchment paper into 12 (for larger donuts) or 16 (for smaller donuts) squares.
7. Transfer the dough to a floured surface and lightly sprinkle the top with flour. Use a bench scraper or sharp knife to cut the dough into 12 equal pieces. For smaller doughnuts, cut dough into 16 equal pieces.
8. Shape each piece of dough into a smooth ball and place on pre-cut squares of parchment paper before transferring to a large baking sheet. Loosely cover the baking sheet with plastic wrap and place in a warm part of the kitchen allowing the dough to double size, for about 30-35 minutes (this timeframe may vary depending on the warmth of your kitchen).
9. Line a cooling rack with two layers of paper towels. Heat the oil in a medium deep bottom pan to 350F. In batches of one or two, carefully place the risen balls of dough into the oil. Use kitchen tongs to remove the parchment square.
10. Fry the dough for 1 – 2 minutes per side or until golden brown. Use a slotted/spider spoon to transfer the donut to the prepared cooling rack. Continue this process until all the donuts are fried.

Vanilla Pastry Cream 

1. In a medium saucepan, add the milk, heavy cream, and salt. Heat the milk mixture under medium-high heat until it starts to simmer.  Remove from heat. 
2. As the milk heats up, add the egg yolks, sugar, and cornstarch to a medium mixing bowl. Whisk ingredients together to combine into a smooth, thick mixture.
3. Place a kitchen towel under the mixing bowl with egg mixture. Slowly pour 1/2 cup of the heated milk in a thin stream into the egg mixture while whisking constantly.
4. Pour the tempered egg mixture into the pot with the remaining hot milk. Bring the custard to a boil under medium heat, whisking constantly, until it starts to thicken and you see boiling bubbles reach the top surface. Remove the pan from heat and strain the pastry cream through a fine strainer into a medium mixing bowl.
5. Whisk in the butter and vanilla extract into the warm pastry cream. Place a sheet of plastic wrap directly over the surface of the cream and refrigerate until thoroughly chilled, about 2-3 hours. 

Caramel Coating and Assembly

1. Use a skewer/chopstick to make an opening at the top of each donut pushing the skewer or chopstick about 2/3 the way into the donuts to create a space for the filling.
2. Give the pastry cream a thorough whisk and transfer it into a large pastry or Ziplock bag. Cut off 1/2 inch from the tip of the bag and fill the donuts with the filling.
3. Make the caramel coating by adding the sugar, water, and lemon juice into a small saucepan under medium-low heat. Whisk the sugar mixture until all of the sugar is dissolved and the mixture starts to gently simmer.
4. Use a dampened pastry brush to remove any sugar granules from the sides of the saucepan. Increase the heat to medium-high. Once the sugar mixture starts to boil, refrain from stirring or whisking. Allow mixture to boil until it reaches a rich golden brown (amber) color.
5. Remove the caramel from heat. Carefully dip the top of each filled donut into the caramel and transfer to a cooling rack to allow the excess caramel to drip off. Please be careful here as the caramel is very hot.
6. If the caramel starts to set before you are done coating the donuts, return the pan back to medium-high heat and swirl in a circular motion until the caramel loosens up.
7. Transfer filled and coated donuts to a large serving plate/platter before serving.