In the bowl of a stand mixer fitted with a dough hook, combine the yeast, warm milk, and 1 teaspoon of sugar. Let sit for 5 to 10 minutes, or until the yeast is foamy.

Add the eggs, cooled butter, flour, remaining 5 teaspoons of sugar, and salt. Stir with a silicone spatula to form a shaggy dough. Place on the stand mixer and mix on medium-low for 5 to 7 minutes until the dough is smooth and gathers around the hook. (It will begin to pull away from the sides of the bowl, but some of it may still stick.)

Scrape down the sides and bottom of the bowl and transfer the dough to a greased bowl or large liquid measuring cup. Cover with plastic wrap or a damp kitchen towel and let rise for 35 to 45 minutes until doubled in size.

Meanwhile, prepare 12 (3-ounce-sized) baba molds. Spray with nonstick baking spray or grease with softened butter and coat with flour, tapping out any excess.

Using two greased spoons, scoop about 2 tablespoons (1½ ounces, 50g) of dough to fill each of the baba mold cavities half full.

Cover with plastic wrap or a damp kitchen towel and let rise for about 20 minutes, until the dough doubles in size and reaches the top of the molds.

Meanwhile, preheat the oven to 375°F. Place the molds on a sheet tray and bake for 12 to 15 minutes until golden brown on top and the internal temperature reaches 200°F.

Let cool for 10 minutes in the pans, then unmold and let cool completely on a wire rack.

While the babas are cooling, in a medium pot, combine the sugar with 1¾ cups (420mL) water. Cook over medium-high heat, whisking frequently until the sugar is completely dissolved. Remove from the heat and let cool slightly (about 15 minutes). Add the rum, lemon juice and vanilla extract and whisk to combine.

Once the babas are just warm, soak 4 to 5 at a time for about 3 to 5 minutes, turning frequently, until the rum syrup has soaked through to the center. (The babas should look visibly bigger, feel heavier and squishy). Transfer the soaked babas to a wire rack set over a sheet tray. Repeat until all of the babas are soaked. Reserve any remaining soaking liquid.

In a medium bowl, whisk to combine the apricot preserves and 2 to 3 tablespoons of water to make a glaze.

Plate one baba on each dessert plate or shallow bowl and brush the tops with the apricot glaze. Serve with whipped cream and an extra drizzle of the rum syrup.