Preheat oven to 350ºF
Place sugar in a small saucepan with 1/2 cup of water and bring to a boil, and simmer for five minutes. Brush down any sugar crystals from the edge of the pan with a brush dipped in cold water. After five minutes remove from heat and allow to cool.
Transfer syrup to a standing mixer and beat at moderate speed for 1 minute. With the mixer running, add in the butter, one tbs at a time. Then add the eggs and egg yolks, also one at a time and continue beating until all the ingredients are combined.
Add in the semolina and beat until smooth, then add the coconut and nutmeg and beat to combine.
Butter and flour a 1.5 quart ring pan with a removable bottom. Using a spatula to help, pour the mixture into the ring pan, making sure to spread it out evenly.
Bake for 1 hour until the cake is golden. Test doneness with a toothpick: you're looking for a similar density at the edges and in the center. Remove from the oven and allow to cool for 25 minutes. Serve cut into thin slices.
Optional: Top with dried coconut strips before serving