Preheat the oven to 350°F.

1. Prepare a leaven with the first three ingredients to obtain a soft dough.

2. Let it rest for 1 hour, covered, in a temperate place.

3. In a robot, mix together the oil, melted butter, lemon zest, and orange zest.

4. Pour in the rum and orange blossom water.

5. Add the eggs and milk to this mixture.

6. Finish by gradually adding the sugar and flour, then incorporate the leaven.

7. Knead for 4 to 5 minutes at medium speed with the robot and let it rise for about 2 hours in an oiled container.

8. Separate the dough and shape 2 brioche, brush with milk, and sprinkle with sugar.

9. Mold the brioche and bake for 45 minutes.