Mix eggs, oil, orange juice, orange zest and sugar. Mix flour and baking powder in a bowl and add the egg mixture. Mix everything with the dough hooks of the hand mixer to a smooth dough.
Cover and leave to rest for about 30 minutes. For the syrup, boil the sugar, stirring constantly, with 3/8 litres of water and orange juice until the sugar is completely dissolved. Let it boil down for about 5 minutes, add honey and let it boil down for another 5 minutes.
Warm the syrup. Form 10 flat balls from the dough with lightly floured hands. Make a hole in the middle of each ball. Heat the fat in a deep fryer to 175 ° C. Hold a wooden spoon in the fat.
When bubbles form, the fat is at the right temperature. Fry the doughnuts in portions for 2-3 minutes until they are crispy brown. Immediately after baking, prick several times with a wooden skewer, dip into the warm syrup and serve.