Day 1: In a bowl of mixer add milk, yeast, sugar, eggs and whisk all together.
Add flour, mix until no dry flour remains, cover and let autolyse for 1 hour.
Start mixing the dough on low speed for 3-4 minutes until well incorporated.
Increase the speed to medium high and continue kneading for 10-15 minutes until the dough looks stronger.
Add salt and mix for a couple more minutes.
Add soft butter, mix for 15-20 more minutes on high speed until the dough comes together.
Cover the dough and let it proof for 2-3 hours at 80F/28C.
Perform 2 stretches and folds during proofing.
Transfer the dough to the fridge for cold fermentation until next day, or at least for 4 hours.
Day 2: Remove the dough from refrigerator.
Prepare muffin tins or donut molds.
If using donut mold, roll the dough 1.5 inch thick, cut the donuts and place them into molds to proof.
If using muffin tins, divide the dough into 12 pieces, round each one, and place into muffin tins to proof.
Cover and let them proof for 1-2 hours at 78-80F/26-28C until puffy.
Prepare the rum syrup by bringing sugar and water to a simmer until sugar dissolves.
Remove from heat, stir in the rum and orange zest strips, let cool down.
To make the glaze, heat apricot jam with rum to liquefy.
Preheat the oven to 350F.
Bake babas for 18-22 minutes until golden brown.
Let them cool and soak each baba into rum syrup for about 30 seconds on each side.
Transfer babas to a cooling rack and pour remaining rum syrup on top.
Brush each baba with apricot glaze.
Prepare chantilly cream by whisking heavy whipping cream with sugar and vanilla until soft peaks.
Serve rum babas by piping whipped chantilly on top, decorated with orange zest strips soaked in syrup.
