Rum Baba (Baba au Rhum)

In a small bowl, microwave milk until between 100℉ and 110℉. Stir in sugar and yeast, and allow to sit for 10 minutes. (Note: yeast may not fully dissolve due to the fat content in milk — this is okay.)
¼ cup warm milk
2 Tbsp granulated sugar
2 ¼ tsp active dry yeast
To the bowl of a stand mixer fitted with the dough hook attachment, add in the yeast mixture, along with eggs. With a fork, mix until well combined.
3 large eggs, at room temperature
Add in flour and salt. Mix on low speed until the dough comes together, scraping down the sides of the bowl as necessary. Increase mixing speed to high and continue mixing until smooth (about 5 minutes more).
1 ⅔ cup all-purpose flour
½ tsp kosher salt
Reduce mixing speed to low and add in softened butter, one Tablespoon at a time, until butter is fully incorporated into the dough (about 2 to 3 minutes).
4 Tbsp unsalted butter, softened
Increase mixing speed to high and knead dough for 5 full minutes (use a timer if necessary). The dough should be slightly less sticky and fairly elastic (i.e. able to pull a good-sized strand without breaking).
Remove the bowl from the stand mixer, scrape down the sides, and cover with plastic wrap. Allow the dough to rise, at room temperature, until it has doubled in volume (about 60 minutes).

Using a pastry brush (or your fingers), grease baba molds with melted butter.
With lightly floured hands, deflate the fully risen dough by pulling at the sides of it with your fingers (it will be quite sticky). Empty the dough onto a lightly floured surface and cut it into small pieces that will fill molds by only ⅓, weighing out the dough for consistency if needed. Set a small piece of dough into each mold, pressing down gently into the bottom and sides of the mold.
Note: I use this 12-cup popover pan (with 2" molds) — each containing approx. 3oz (85g) — so I weighed each piece of dough to approx. 1 oz (28g). If you have leftover dough (as I did), use additional molds or keep in the refrigerator for later use. (Do not overfill by more than ⅓.)
Set the molds on a baking sheet and cover with a piece of plastic wrap greased with melted butter (to prevent sticking). Allow the dough to rise a second time, just until it has reached the rim of the molds (about 25 to 30 minutes).
While dough is rising, preheat oven to 375℉.
Once risen, remove plastic wrap and bake in the centre of the oven until golden brown (about 11 to 15 minutes). If using individual molds, make sure they are evenly spaced out on baking sheet to allow for proper air circulation.
Remove baking sheet from oven and allow babas to cool in the molds for 5 minutes, before removing babas from the molds and allowing them to cool completely on a wire rack.

In a saucepan, add in sugar, water, and vanilla pod with the seeds removed (or vanilla extract). If desired, add in orange zest and orange juice.
1 cup granulated sugar
2 cups water
1 vanilla bean, seeds removed
Zest of 1 medium orange (optional)
Juice of 1 medium orange (optional)
Set the saucepan over medium heat and swirl the pan until all of the sugar has dissolved. Bring the syrup to a simmer and allow it to simmer for 5 minutes.
Remove the pan from the heat and set it on a wire rack. Allow the syrup to cool until lukewarm (about 25 to 30 minutes).
Once lukewarm, strain syrup into a large bowl or dish (to remove the orange zest and vanilla pod).
Stir in rum.
½ cup good-quality dark rum
Set the babas in the syrup, submerging and rotating them until they absorb the syrup (about 5 minutes). They will float at first, but will become heavier and sink slightly as they absorb the syrup. You can also use a small toothpick or wooden skewer to poke holes in the babas, if desired.
Set the engorged babas on a wire rack over a sheet pan. With a spoon, pour any remaining syrup over the top of each baba. Allow them to sit, and for any excess syrup to drip off, for about 30 minutes.

In the meantime, in a saucepan, heat apricot jam over medium heat until loosened (about 2 to 3 minutes).
½ cup good-quality apricot jam
Press apricot jam through a sieve to remove any larger pieces of apricot.
In the same saucepan, mix sieved apricot jam, sugar (depending on sweetness of jam), and rum.
1–2 Tbsp granulated sugar
1 Tbsp good-quality dark rum
Cook over moderate heat until thickened and sticky (about 3 to 5 minutes). Allow to cool slightly.
Using a pastry brush, brush each baba with the apricot glaze and set on a plate. Cool the babas in the refrigerator for at least 1 hour.

In the bowl of a stand mixer fitted with the wire whip attachment, combine heavy cream, reserved vanilla seeds (or vanilla extract), and powdered sugar.
1 cup heavy whipping cream, chilled
2 Tbsp powdered (icing) sugar
Scraped seeds from 1 vanilla bean
Mix at high speed until soft peaks form. Serve immediately with chilled babas.