Whisk together the melted butter, vanilla essence, milk, water, sourdough starter, and egg until combined well.
Mix the dry ingredients in a large bowl.
Mix the wet with the dry ingredients.
The dough will be very wet—don’t add more flour. Lightly oil the top and let it rise in a warm place for 5-6 hours.
Once doubled in size, flour a surface generously, tip out the dough.
Flour the top of the dough generously and cut wide strips (around 6cm ~2¼ inches) using a bench scraper or large knife.
From the strips, cut smaller pieces perpendicularly around 3cm (~1¼ inches) wide and shape into oval shapes (around golf ball size).
Place each oval 1-2cm apart on a greased or floured baking tray.
After shaping the dough, let it rest for 10-20 minutes.
While the dough rests, heat oil to 180°C (350°F), then lower the temperature sligthly and fry the dough balls, about 3 minutes per side, until deep golden brown.
Place the fried dough balls on a cooling rack or tray lined with paper towel to soak up the excess oil.
Make the syrup by simmering all syrup ingredients on low heat for 10-15 minutes. Do not let it boil rapidly. The syrup should remain watery and not get thick.
Steep the fried dough balls in the simmering syrup for 3-4 minutes per side.
Roll each ball in desiccated coconut.
Serve warm or store in an airtight container for max 1-2 days.