MAKE THE DOUGHNUTS

1. Sift flour into a bowl (or bowl of your stand mixer) and set aside. Warm milk on the stove or in microwave until it’s warm, but not hot, to the touch. Stir in one teaspoon of sugar and all of the yeast. Set aside until the yeast gets bubbly.
2. Meanwhile take another bowl and whisk together reaming sugar with egg yolks, egg, butter, vanilla, rum, salt and lemon zest.  Stir the yeast mixture into the flour slowly, then pour in the egg mixture and knead dough with a dough hook for a few minutes until the dough comes together and pulls away from the sides. The dough will be somewhat sticky, but it should be smooth with no patches of flour visible. Give it a light knead with your hands then transfer it to a large oiled bowl. Cover loosely with plastic wrap and transfer to the refrigerator. Let proof overnight. 
3. Shape doughnuts: 
   The next day, take the dough out of the refrigerator. Remove it from the bowl and place it on a lightly floured work surface. Slice it into 12 equal pieces (each should weigh between 2.5-3 ounces or 70-80g). Shape each piece into a ball and place it on a piece of parchment paper (or silpat) dusted with flour. Leave enough room between all the dough balls, as they will rise. Cover the dough with a light kitchen towel (or plastic wrap) and let rise until doubled in size, about 2 hours. 
4. Fry:
   Pour oil into a large pot suitable for frying (I’m using a cast iron skillet, enamel cookware works nicely too), set over medium heat. Bring the temperature of the oil to 320-340°F (160-170°C). Using a thin spatula, pick up one doughnut at a time and place it into the hot oil. You can fry 2-4 at a time, depending on your skillet size. Fry on the first side for 2-3 minutes, then flip over and fry another 2 minutes, until doughnuts are golden brown on the second side too. 
5. Place fried doughnuts on a platter/pan lined with paper towels. If using granulated sugar, dip and swirl warm donuts into granulated sugar. If using powdered sugar, wait until the end. 
6. Let doughnuts slightly cool. Fit two pastry bags with plain round tips (medium sized). Fill one with pastry cream and one with strawberry jam. Pierce each doughnut on the side (on the white line) and fill it first with jam, then with vanilla (or the other way around). Set on a serving platter. Dust with sugar, if desired, and serve. 

MAKE VANILLA CREAM (I like to make this after the dough is in the refrigerator and then let it set overnight along with the dough):

1. In a medium bowl, whisk egg yolks, sugar, corn starch, vanilla and salt until fluffy and pale, a few minutes. Warm milk on the stove over medium heat until it barely comes to a simmer. Slowly pour the milk into the egg mixture, while whisking constantly. Transfer the mixture back to the saucepan and cook over medium heat until the mixture is bubbly and thick. This should take about 5 minutes. 
2. Once the vanilla cream is thick, remove it from heat, stir in the butter until it’s melted. Transfer it to a glass container, cover with plastic wrap (so that it touches the cream) and first let cool to room temperature. Then store it in the refrigerator overnight. (This will thicken it even more.)