Sift the flour into the bowl of your stand mixer, a KitchenAid, or in a big bowl if you don’t have one. Add salt and oil.
Combine well until it forms a granulated mixture. First, start on a low speed and then increase the speed to 2 or 3.
Add the wine to the flour mixture until well combined.
Remove the dough from the bowl, and knead it until a smooth and elastic dough.
Wrap it in plastic wrap and set aside for about 20-30 minutes. If it’s hot out, put the dough in the fridge.
Cut walnut-sized pieces of dough and roll them out into 2.5-inch (6cm) ropes. Work quickly so the dough doesn’t get too warm. If everything is ok, you should have smooth ropes without any cracks.
If they fall apart, knead the dough again with a splash of water and set aside for a little time, then starts rolling out again.
Join the ends of the ropes to form a sort of small ring, press to seal.
Place them on a parchment-lined baking tray.
If it’s hot out, refrigerate your taralli for about 1 hour (they won’t get flat).
In the meantime, bring the water to a rolling boil and add coarse salt.
Cook about 10 or 12 taralli at a time: Drop them into the water.
Stir the water with a wooden spoon without touching the taralli, just whirl the water.
As soon as the taralli float on the surface (it takes about 1 minute), take them out with the skimmer and place them onto a tray lined with a clean tea towel; repeat the process until you have cooked all the rings.
Let them rest for at least 4-5 hours before baking them. The more they rest, the better they are. They may also be set aside in a cool place overnight, but that depends on the time you have. If you are in a hurry, bake them right away.
Transfer the taralli onto a parchment-lined baking tray.
Preheat the oven to 375°F (190°C) and place the tray on the middle rack. Bake them for about 20-25 minutes or until light golden.
Take them out of the oven and be patient; let these delights cool down completely before eating.