Place the olive oil in a small saucepan at low heat. Add the lemon and orange peel and the cinnamon stick and simmer for about 10 minutes.
Add the grains of anise and continue simmering for a few more minutes. Remove from the heat and set aside to cool down.
In a skillet, toast the sesame seeds, being careful not to burn them.
Sieve the flour over a large mixing bowl. Add the salt and mix. Add the white wine and the flavored oil (use a colander to hold the solids) and mix. You can do this by hand or using a stand up mixer.
Add the orange juice and the toasted sesame seeds and continue mixing until it becomes harder to continue mixing. Bring the dough to a floured surface and continue working it with your hands until it becomes elastic and not sticky. Cover with plastic or a cloth and let rest for about 30 minutes.
Using a rolling pin, roll the dough on the floured surface to a thickness of about 1/4 inch.
Cut the dough into 2x2-in squares
Shape each square into the pestiño shape by holding two facing corners together.
Working in batches, fry the pestiños in abundant olive oil until golden. Remove from the oil and place them on a plate lined with paper towels to absorb the excess oil.
While the pestiños cooling down, in a shallow plate mix the ground cinnamon and granulated sugar. Roll the pestiños into the sugar-cinnamon mix until completely coated.
Notes
Only use the outer layer of the citrics, avoiding the white part
First peel the orange, to get its peel, then squeeze its pulp, to get its juice —both used in the dough