Soak the Raisins: In a heatproof bowl, combine the boiling water and raisins, cover and let soak for a minimum of 30 minutes. Drain and set aside, reserving a ¼ cup (2 fl oz/60 ml) of the soaking liquid.
Whisk the reserved soaking liquid with the 4 eggs and set aside.
In the bowl of a stand mixer fitted with a dough hook (or by hand with a large bowl and wooden spoon), combine the flour, sugar, yeast and salt.
Work in the butter until the mixture is crumbly, then stir in the egg mixture followed by the drained raisins. Knead until you have a soft, smooth but very sticky dough that just comes together, about 5 minutes.
Place in a large, oiled bowl, cover, and let rise until doubled, about 60-90 minutes.
Make the Rum Syrup: In a small saucepan, combine the water, sugar, honey, orange zest and cloves and bring to a simmer over medium-high heat.
Lower the heat to allow the syrup to very gently simmer for 10 minutes, then remove from the heat, stir in ¾ cup (6 fl oz/180 ml) of rum and the vanilla extract. Cover the pot and let the syrup cool.
Shape and bake the babas: once the dough has risen, butter a 12-cup muffin tin.
Divide the dough into 12 equal pieces (2 oz/57 g) and on a lightly floured work surface, roll each into a ball and place in a muffin cup. Cover gently with plastic wrap and let rise again until doubled in size, about 30 minutes.
Towards the end of the rising time, preheat the oven to 375°F (190°C).
Bake the babas for 20-25 minutes, until golden brown. If not serving right away, let cool and then store in an airtight container.
Soak the Babas: Two hours before serving, place the babas upside down in a baking dish and pour the syrup over them. Turn the babas in the syrup a few times to allow them to fully soak up the syrup.
To serve, place a baba on a serving dish, drizzle with about 1 tablespoon of rum and a dollop of lightly whipped cream.