In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour and salt.
Stir in the oil, Cachaça, and vinegar.
Slowly add the cold water until the dough comes together.
If too dry, slowly add a little more water. If too sticky to handle, slowly add a little more flour.
On a floured work surface, knead the dough until smooth and elastic. Cover and allow to rest in the refrigerator for 30 minutes to 1 hour.
To assemble:
In a large bowl, combine the mozzarella and parmesan cheese.
Divide the rested dough in half. Place one half on a floured work surface and cover the other.
Roll the dough in a very thin sheet about 1/16 inch (1.5 millimeters) thick.
Use a 4-6 inch (10-15 centimeter) circular cutter to cut out round wrappers from the dough. Lightly dust with flour as needed to prevent sticking.
Place about 1 tablespoon of the shredded cheese in the center of one circle.
Fold the circle in half over the filling, pressing out any air and press together the edges to seal. Press a fork around the edges to seal further. Repeat with remaining circles and remaining dough.
Fill a pot or deep fryer with at least two inches (5 centimeters) of vegetable oil and heat to 350˚F (180˚C).
Add a few of the prepared Pastéis at a time, being careful not to overcrowd. Fry on each side until crisp and golden, about 3 minutes total. Be careful not to overcook or the filling may burst.
Remove to a towel-lined plate with a slotted spoon. Repeat with remaining Pastéis.
Serve the Pastel de Queijo warm. Caution: the melted cheese will be hot straight out of the oil.