Beat shortening and sugar together in a large bowl using an electric mixer until creamy. Add eggs, orange zest, and vanilla extract.
Combine corn flour, baking powder, cinnamon, and flour in another bowl. Stir and add 1/2 of the mixture to the shortening mixture. Beat on low speed until combined. Add the remaining flour mixture and knead with your hands until dough is combined.
Preheat the oven to 350 degrees F (175 degrees C).
Roll a small portion of the dough into a thin log; pinch ends together to form a small ring. Place on a baking sheet. Repeat with the rest of the dough. Place coricos as closely together on the baking sheets as you like; they do not spread.
Bake in the preheated oven until coricos are golden brown all over, about 45 minutes. Remove and let cool.
