In a Stand Mixer bowl, add the olive oil and the wine and mix the two.
Add the flour and continue to mix until the flour and the liquids are completely amalgamated and the dough is firm. Work it for about 15 mins.
Move the dough to a working table. Cut a small piece and by hand roll it into a thin long strip about 1/4 thick.
Cut the strip into sections about 1" long and connect the two ends by pressing them together with your fingers.
Make all your Tarallini and place them on a baking sheet. Bake them for 30 mins. at 375F.
After you have baked all your Tarallini, make your icing by melting the water and sugar in a pot over the stove, stir and let the water boil. Once the water boils, continue stirring and, once you stop stirring and the bubbles do not disappear from the surface (about 5 minutes), the icing is ready.
Put 5 spoons of liquid in a steel bowl, add a handful of Tarallini at the time and tumble them with a wooden spoon several times until they get coated with the icing.
Pour the Tarallini on a wood board. Repeat the process for the remaining Tarallini and pour them on top of the other Tarallini. Leave them to dry for several hours until the icing is completely dry and turns white.