Pour the warmed milk into a small bowl and sprinkle the yeast and 1/2 teaspoon of sugar over it. Let it sit for 5 to 10 minutes until it becomes foamy on top.

In your stand mixer bowl, whisk together the flour, remaining sugar, and salt.

Add the yeast mixture to the dry ingredients along with the eggs and vanilla. Using the dough hook on medium-low speed, mix for about 2 minutes until a shaggy dough forms.

With the mixer still running on medium-low speed, add the softened butter one tablespoon at a time over about 3 to 4 minutes. Continue mixing for 5 to 7 minutes total after all butter is added until the dough is smooth and silky.

Lightly butter your baba molds or a muffin tin with 6 cups. If using muffin tins, use only every other cup to give the babas room to rise.

Divide the dough evenly among your prepared molds, filling each about halfway. Cover loosely with a clean kitchen towel and place in a warm, draft-free spot for 45 minutes to 1 hour until the dough rises to the top of the molds.

Preheat your oven to 375 degrees Fahrenheit. Once the dough has risen, bake for 12 to 15 minutes until the babas are golden brown on top and spring back when gently touched.

While the babas bake, in a saucepan combine 1 cup sugar and 1 1/2 cups water. Bring to a boil, stirring occasionally until the sugar dissolves completely, then remove from heat. Stir in the rum, orange zest, and vanilla extract and let the syrup cool for about 10 minutes.

Remove the babas from the molds and place them in a shallow dish. Slowly pour the warm syrup over each cake, turning them gently to soak all sides evenly. Let them sit for at least 30 minutes to absorb the syrup fully.

In a clean bowl, whip the heavy cream with the powdered sugar until stiff peaks form, about 2 to 3 minutes with an electric mixer.

Place each soaked baba on a serving plate and top with a generous dollop of whipped cream. Add candied orange slices if desired. Serve immediately.