In a large mixing bowl, combine the cornmeal, all-purpose flour, salt, and sugar. Mix until well incorporated.
Gradually pour in the boiling-hot water, stirring until a smooth dough forms.
Add the salted butter (or vegetable oil) and mix until fully incorporated.
Form the dough into small balls, about the size of a golf ball, making around 12 dumplings.
In a large pot, bring the chicken or vegetable broth to a gentle boil.
Gently drop the dumplings into the boiling broth and cook for 10-15 minutes until they float.