METHOD
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dough
Add flour and sugar to a bowl of a stand mixer fitted with a dough hook. Feel free to use a hand-held electric mixer fitted with two dough hooks. Make a well in the middle. Pour lukewarm milk and lukewarm water into the well. Add the active dry yeast and cover the ingredients with some flour. Add the eggs, grated lemon zest, rum, and salt. Start kneading on low, set the stand mixer to medium speed, and knead for about 6 - 8 minutes or until the dough is elastic, smooth, and easily separates from the bowl. Add the butter and knead for another 3 - 4 minutes for the butter to incorporate into the dough and separates from the bowl easily.
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first proofing
Cover the bowl with the dough with clingfilm and leave to rise at room temperature (20 - 25°C / 68 - 77°F) until visibly increased for about 2 hours. Then transfer to a fridge and leave to proof overnight, covered, for up to 12 - 16 hours.
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second proofing
Prepare a large baking sheet. Cut 14 (10 cm x 10 cm (4-inch x 4-inch) squares from parchment paper and place them on the baking sheet. Divide the dough into 14 pieces. Each piece should weigh around 65g / 2.1 ounces. Shape each piece into a smooth ball. Place the balls seam-side down onto the prepared parchment paper on the baking sheet and repeat until all the balls are shaped. Leave enough space between the doughnuts to rise. Cover with a kitchen towel. Lightly sprinkle the towel with water. Leave the doughnuts to rise at room temperature for about 1 1/2 hours - 2 1/2 hours or until they triple in size.
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frying
Place a large pan (with a lid) over medium heat. Add the oil and wait until the oil reaches 170 - 180°C / 340 - 355 °F. Carefully pick one doughnut with the parchment paper. Turn it around in your hands so the seam looks up, gently drop it into the oil, discard the paper. Add about 4 - 5 more doughnuts, depending on the pan size. The doughnuts should have some space to move, but not too much. Shake the pan slightly to distribute the doughnuts. Cover with a lid and fry for 2 - 3 minutes at 160 - 170°C / 320 - 340 °F, then remove the lid, turn the doughnuts, and fry for another 2 - 3 minutes (uncovered). Transfer the doughnuts onto a paper towel-lined wire rack. Repeat the process until you fry all the doughnuts.
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vanilla cream
Add the egg yolks, sugar, flour, and vanilla to a bowl. Using a whisk, mix into a smooth mixture. Pour boiling milk over the mixture and stir well to get a combined mixture. Transfer to a saucepan and place over medium-high heat. While constantly whisking, cook for 2 - 3 minutes for the mixture to thicken. The consistency should be smooth. Remove from the heat and transfer to a bowl. Pour water or add ice to a large bowl and place the bowl with the cream over the water/ice. Immediately add the cold butter while the cream is still hot and whisk well to incorporate.
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tiramisu cream
Add the mascarpone to a bowl and add the prepared vanilla cream. Stir in the grated orange zest, salt, and freshly squeezed orange juice. Beat well with an electric mixer to combine.
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serve
Make a hole in each doughnut. Add a teaspoon of freshly brewed coffee and fill it with tiramisu cream. In a small bowl, combine cacao and powdered sugar and dust the doughnuts with the mixture.