Prepare the Doughnut Dough:

1. Activate the Yeast: In a small bowl, combine the warm milk and granulated sugar. Stir to dissolve the sugar, then sprinkle the yeast over the milk. Let it sit for 5-10 minutes until it becomes foamy and bubbly. This step ensures that the yeast is activated.
2. Make the Dough: In a large mixing bowl, whisk together the flour, salt, and cinnamon (if using). Once the yeast mixture is ready, pour it into the flour mixture. Add the eggs, melted butter, and vanilla extract. Stir the ingredients together until a dough begins to form.
3. Knead the Dough: Turn the dough onto a lightly floured surface and knead for about 5-7 minutes, or until the dough is smooth and elastic.
4. Let the Dough Rise: Form the dough into a ball and place it in a greased bowl. Cover the bowl with a damp cloth and let it rise in a warm place for about 1 hour, or until it has doubled in size.

Shape the Doughnuts:

5. Roll Out the Dough: Once the dough has risen, punch it down to release the air. Transfer it to a floured surface and roll the dough out to about ½ inch thickness.
6. Cut the Doughnuts: Use a doughnut cutter or two round cookie cutters (one large and one small) to cut out doughnuts and holes. You should have about 12 doughnuts. Re-roll any leftover dough and cut out more doughnuts if needed.
7. Let the Doughnuts Rest: Place the cut doughnuts on a baking sheet lined with parchment paper and let them rest for about 15-20 minutes to allow them to puff up slightly.

Fry the Doughnuts:

8. Heat the Oil: In a deep fryer or large pot, heat vegetable oil to 350°F (175°C). You’ll need enough oil to fully submerge the doughnuts.
9. Fry the Doughnuts: Carefully place the doughnuts into the hot oil, one or two at a time, to avoid overcrowding. Fry for 1-2 minutes on each side, or until golden brown. Use tongs to remove the doughnuts and place them on a paper towel-lined plate to drain excess oil.

Make the Whipped Caramel Filling:

10. Prepare the Caramel: In a saucepan over medium heat, combine the heavy cream, brown sugar, butter, and salt. Stir frequently until the sugar has dissolved and the mixture begins to simmer. Let it cook for about 5 minutes until it thickens slightly.
11. Whip the Caramel: If you prefer a thicker caramel filling, dissolve the cornstarch in a small amount of water and add it to the saucepan. Stir the mixture until it thickens to your desired consistency. Remove from heat and stir in the vanilla extract. Allow the caramel to cool to room temperature before using.

Assemble the Doughnuts:

12. Fill the Doughnuts: Once the doughnuts have cooled slightly, use a piping bag with a filling tip to inject the whipped caramel filling into the center of each doughnut. If you don’t have a piping bag, you can also use a small, sharp knife to make a hole in the doughnuts and spoon in the filling.
13. Coat the Doughnuts: For an extra touch of sweetness, you can roll the doughnuts in powdered sugar or drizzle them with more caramel sauce before serving.