In a large mixing bowl, add the flour and salt and pour in the olive oil.
Mix the vinegar and water, and mix that into the flour.
If the mixture is crumbly, add 1 tbsp of water, and keep mixing. Repeat until the dough looks like an elastic ball.
Keep kneading until the dough pulls away from the side of the bowl.
Transfer to a clean bowl, cover with 1 tbsp oil and cover. Let it rest 30-60 minutes.
Phyllo
Divide the dough into 6 even parts.
Sprinkle some flour (semolina if you have) on your work surface,
Slowly work the dough ball into the shape you want, starting with fingers, and moving to a rolling pin. Sprinkle flour (or semolina) if the dough is too sticky.
Make sure to turn the dough over a few times durring the rolling process to ensure it does not end up stuck on your work surface.
Assembling the x-pita
Brush the bottom and sides of your baking pan with olive oil.
Place the first sheet of phyllo.
Brush with oil, and place another sheet of phyllo on top.
Repeat brushing and layering.
Spoon in the filling.
Cover with remaining 3 sheets, brushing with olive oil between each layer.
Roll up the overhang into something pretty, don't be afraid to trim some off with a knife.
Score into pieces of the desired size (just the top 3 layers).
Brush the top with more olive oil.
Baking
Bake at 390F around 50 minutes (until golden brown).
Let cool slightly before serving.
Notes
The vinegar prevents the formation of gluten, and keeps the phyllo more flaky instead of chewy like a traditional pita for a gyro.