Mix flour and salt in a bowl. Drizzle the oil over the flour. Mix the oil in quickly so drops of the oil are dispersed throughout the flour.
Trickle in water, a bit at a time, and knead until a smooth, supple dough forms. Place in the bowl, cover and set aside for at least 30 minutes.
Turn out the rested dough on a floured surface and dust a rolling pin with flour.
Roll the dough into a rectangle about 14 inches long and 12 inches wide. Brush with melted butter all over and sprinkle a bit of flour.
Working along the shorter edge, lift the dough and fold it over itself, then repeat for the other side, creating three distinct layers.
Brush the folded dough with butter, sprinkle flour, and then fold into thirds again.
Roll out the folded dough, again to a rectangle about 14 inches long and 13 inches wide. Brush with butter all the way to the edges and sprinkle flour.
Starting on the short side, roll the dough into a tight cylinder. Cut the cylinder into 12 equal pieces.
Flour the surface very lightly, if needed, and roll out a paratha about five inches in diameter.
Heat a non-stick griddle or cast-iron griddle over medium high heat. Place the paratha on it and let it cook until it begins to bubble.
Flip over and brush with a bit of vegan butter. Once the underside has golden-brown spots, flip again and cook the other side. Brush some butter again if you wish.
As soon as the paratha comes off the stove wrap it in a kitchen towel. Once all the parathas have been cooked, pick them up, still in the towel, and crush them between your palms. This step helps separate the layers and makes the parathas softer. Serve the parathas immediately.