Funny! After looking up the New Orleans style recipe some last words about this down to earth subject.
The New Orleans recipe equals the also existing Congolese recipe (a Congolese woman friend made them in my kitchen) This recipe can't be a derivation from the Belgian 'smoutebol' migrated to the U.S. through the slave trade, as the European exploration and administration of Congo took place from the 1870s. Slave trade act is from 1807. It may be just a coincidence.

In one of the recipes the N.O. style beignets were referred to as "square donuts", i.e "square balls".
Would it be: A plane figure having four equal sides?
Or this: A square meal.