In the bowl of a stand mixer fitted with the dough hook attachment, combine the bread flour, olive oil, white wine vinegar, honey, and salt. Start the mixer on a low speed and gradually add the water until the mixture comes together to form a dough. Adjust the water as needed, depending on the flour and environmental conditions. Once the dough has formed, increase the mixer speed to medium and knead for about 5 minutes until the dough is soft, elastic, and slightly tacky but not sticky.
If you don’t have a stand mixer, combine the ingredients in a large bowl. Once mixed, transfer the dough to a floured surface and knead by hand for about 10 minutes until it reaches the desired consistency.
Shape the dough into a ball and place it in a clean, lightly oiled bowl. Cover the bowl with a damp cloth or plastic wrap and let the dough rest for 45 minutes. This resting period allows the gluten to relax, making it easier to roll the dough out thinly later.
After resting, turn the dough out onto a lightly floured surface. Divide it into 8 equal portions. Shape each portion into a small ball.
Working with one ball at a time, press it down into a flat disk with your hands. Lightly flour your work surface and rolling pin with either semolina or all-purpose flour. Roll out the dough, turning and flipping it frequently, and adding more flour as needed to prevent sticking. Aim to get the dough as thin as possible, ideally so thin that you can see your hand or the countertop through it.
Once rolled out, the phyllo sheets can be used immediately in your favorite recipes. If layering, brush each sheet lightly with melted butter or oil to prevent them from sticking together and to achieve that characteristic flaky texture when baked.
Follow the baking instructions for your chosen recipe. Typically, phyllo dough bakes well at a high temperature (between 375°F to 400°F or 190°C to 200°C) until golden brown and crisp.