01 -  Combine lukewarm milk and active dry yeast in a small bowl. Allow mixture to stand for 5 minutes until foamy. 
 02 -  Whisk together flour, granulated sugar, and salt in a large mixing bowl. Incorporate eggs and milk-yeast mixture, blending until smooth. 
 03 -  Beat softened butter into the dough gradually until fully absorbed and the mixture becomes glossy and elastic. 
 04 -  Cover the bowl with a clean towel and let the dough rise in a warm location for 1 hour, until doubled in volume. 
 05 -  Preheat oven to 350°F (180°C). Grease 8 small baba molds or muffin tins with unsalted butter. 
 06 -  Evenly divide the risen dough among molds, filling each approximately halfway. Allow to rise uncovered for 20–30 minutes until visibly puffy. 
 07 -  Bake in preheated oven for 15–20 minutes, or until golden brown and springy to the touch. Remove and unmold onto wire rack to cool slightly. 
 08 -  While babas bake, simmer water with granulated sugar in a small saucepan until dissolved. Remove from heat and stir in white rum and dill pickle juice. 
 09 -  Immerse warm babas in pickle juice rum syrup for 1 minute, rotating to ensure even absorption. Transfer to wire rack to drain. 
 10 -  Beat heavy cream, powdered sugar, and vanilla extract with electric mixer until soft peaks are formed. 
 11 -  Plate babas, topping with whipped cream. Garnish with thin pickle slices and fresh mint leaves if desired.