In the bowl of a stand mixer, combine the all-purpose flour, cinnamon, yeast, and sugar. In a liquid measuring cup, mix the warm whole milk, salt, and vanilla. Add this milk mixture and the beaten eggs to the dry ingredients in the stand mixer bowl. Using the stand mixer with the dough hook attachment, gradually incorporate the dry ingredients into the wet ones until a shaggy dough forms. Add the softened butter and shortening to the mixing bowl, and continue to knead the dough in the stand mixer until it becomes smooth and elastic; approximately 5 minutes, the dough will be soft.

Once done, lightly oil your hands and transfer the dough to a greased bowl. Cover it with a damp towel and allow it to rise in a warm, draft-free place for about an hour until it doubles in size. After rising, punch the dough down, transfer it to a floured surface, and divide it into pieces weighing around 100g each. Using a rolling pin, roll each piece until it's about ½ inch thick.

Preheat a griddle or non-stick skillet over medium heat. Place each gordita on the heated surface and let them cook until lightly brown and firm, about 2 to 3 minutes for the first side. If you're using a skillet, cover them with a glass lid while they cook.

Carefully flip the gordita to the other side and continue cooking for an additional 2 to 3 minutes, making sure to cover it with the glass lid during this process as well. To prevent burning and ensure even browning, flip the gorditas a few times during cooking.

Once they are evenly browned and firm on both sides, transfer them to a plate lined with a clean kitchen towel. Cover the cooked gorditas with another clean kitchen towel to keep them warm; this will also allow any residual steam to gently cook the bottom ones. Serve your freshly cooked gorditas while they are hot. Pair them with your choice of either dulce de leche or butter. Enjoy!