In a saucepan, bring water with salt and sugar to a boil.
Remove from heat, quickly stir in cornmeal until it forms a smooth dough.
While warm, mix in the grated Edam cheese until fully incorporated.
Allow dough to cool, then scoop and roll into small, finger-sized logs (about 3 inches).
Heat oil to 350°F; fry sorullitos in batches until golden brown and crispy (approx. 2-3 mins). Drain on paper towels.