How to Make It
In a small bowl, stir together the milk, yeast and 1/3 cup of the flour with a fork until smooth. Set the mixture aside until small bubbles appear, about 10 minutes.
Butter six 1/2-cup baba molds or muffin tins. In the bowl of a standing mixer fitted with a whisk, combine the eggs, sugar, salt and the remaining flour. Add the softened butter and beat on medium speed for 10 minutes. Add the yeast mixture and the water and beat for 1 minute. Using a rubber spatula, scrape the dough from the whisk and scrape down the side of the bowl. With moistened hands, fill the prepared baba molds two-thirds full with the yeast dough. Set the molds in a warm place and let rise until the dough just reaches the rims, about 20 minutes.
Preheat the oven to 350°. Bake the babas for about 15 minutes, or until puffed and golden brown. Remove from the oven and immediately turn the babas out onto a wire rack to cool completely.
In a small saucepan, combine the water and sugar and bring to a boil over moderately high heat; cook until the sugar has dissolved. Transfer the syrup to a bowl and add the lemon verbena and rum. Let the syrup cool to room temperature.
Arrange the babas in a large, shallow dish and pour the syrup on top. Baste the babas with the syrup, turning occasionally, until they have absorbed as much syrup as possible without falling apart, about 25 minutes. Remove the babas from the syrup.
Cut each baba in half lengthwise and place on dessert plates. Surround the babas with peach wedges and serve.