In a large bowl, mix the warm water, coconut milk, yeast, sugar, and salt until dissolved. Set aside for 5 minutes to activate the yeast.
Lightly beat the egg into the yeast mixture.
Mix 3 cups of flour, the grated coconut, cardamom, and nutmeg by hand or in a stand mixer.
Turn the dough out onto a lightly floured surface, and knead until fully incorporated and it's not too sticky to the touch (5-7 minutes). Gradually adding more flour if needed, but it's better to err on the side of less flour than more.
Place the dough in a greased bowl, turning once to coat. Cover loosely with a clean cloth and let it rise in a warm, draft-free place for 1-2 hours or until doubled in size.
Punch the dough down, divide into 4 equal pieces, then form balls and roll out each piece into 6 triangular pieces. Let it rest for about 15 minutes.
Fill a large saucepan with vegetable oil until it's at least 3 inches (about 5 centimeters) deep (too little will result in flatter mandazi). Heat the oil over medium heat until it reaches 375℉ (190℃).
Gently drop the mandazis into the oil in batches to avoid overcrowding the pan.
Fry for a few minutes until the bottom side is golden brown, quickly turn them over and fry for a few more minutes until the other side is golden brown.
Remove them from the oil with a large slotted spoon or spider (culinary, not the arachnid). Place them on paper towels right away to soak up the excess oil.
Sprinkle with powdered sugar to make them sweeter if desired.