1In a large bowl, mix flour with dry yeast, sugar, eggs, and warm milk. Incorporate melted butter and knead until you get a soft, smooth dough.
2Cover the bowl with a clean towel or plastic wrap and let the dough rise in a warm place for 1 hour, or until doubled in volume.
3Grease individual baba molds or ramekins with butter. Divide the risen dough equally among the molds, filling them halfway.
4Place the molds in the air fryer basket. Bake at 180°C (350°F) for 12 minutes, until the babas are golden and a toothpick inserted in the center comes out clean.
5While the babas bake, prepare the rum syrup: in a small saucepan, combine water, sugar, and vanilla bean (if using). Heat over medium heat, stirring until sugar dissolves, then bring to a boil. Remove from heat and add dark rum.
6Immediately after removing the babas from the air fryer, generously brush them with the warm rum syrup while they are still hot, so they absorb the liquid well.
7Just before serving, whip the heavy cream with powdered sugar until stiff peaks form. Place a dollop of whipped cream on top of each syrup-soaked baba.