100 ml dark rum (1/3 cup + 1 tbsp), plus more to drizzle
Glaze: 3 tbsp apricot jam, warmed
Whipped cream (Chantilly), to serve
How to make it
Dough (15 min plus 45 min): Beat the flour, yeast, sugar, salt, eggs and milk in a mixer 8 minutes into a very soft, elastic batter-dough. Beat in the butter until glossy. Cover and rise 45 minutes.
Fill moulds (10 min): Butter 10 baba moulds or a muffin tin. Pipe or spoon the dough in, filling halfway.
Proof (45 min): Proof until the dough reaches the rims.
Bake (20 min): Bake at 180C (350F) 18 to 20 minutes until deep golden. Unmould and leave to dry on a rack (overnight is ideal; dry babas soak better).
Syrup (10 min): Simmer water, sugar, peels and vanilla 5 minutes, take off the heat and add the rum. Keep it warm (about 60C).
Soak (15 min): Drop the babas into the warm syrup, a few at a time, and turn them for a minute or two, until heavy and soaked through. Drain on a rack over a tray.
Finish: Brush with warm apricot jam. Serve with whipped cream and an extra splash of rum at the table.
Tips
Dry babas drink more syrup; bake them a day ahead.
Warm syrup, not boiling: boiling makes them fall apart.