Make the puff pastry:
Place the two cold sticks of butter, straight out of the fridge, on a chopping board or the kitchen platform. Sprinkle the 1/4 cup of all-purpose flour over it and, using a rolling pin or something heavy, beat the butter until it flattens out quite a bit but is still quite solid.
Pat the edges of the butter to form a square. Place in a container and refrigerate for at least 30 minutes.
In a bowl, place the 2 cups of flour, salt and, using enough water, knead into a smooth and pliable dough.
Allow the dough to rest for a few minutes, then roll it out into a square large enough so you can wrap the square of butter in it.
Once you have wrapped the butter, making sure it is well-sealed, then roll out the dough into a rectangle about 7 inches wide and 10 inches long. Do this preferably on a metal baking sheet so you have a cool surface and also so you can easily transfer the dough to the fridge. The rolling might take a little work because the dough can be resistant, but be patient.
Now lift the edges of the rectangle along the long side and fold over one another so you have three layers. Place the sheet with the puff pastry in the fridge and let it stand for at least 15 minutes. Then remove and roll out again and fold again to make three more layers. Repeat four more times.
After you've let the dough stand in the fridge for the last time, divide the puff pastry into two. Freeze half and use the rest for the vegetable puffs.
Make the filling:
Heat the oil and add the cumin seeds and asafetida. When the cumin sputters and crackles, add the ginger, stir-fry for a few seconds, then add the turmeric. Stir quickly to mix, stir in the chillies, then add the potatoes.
Saute, stirring frequently, for a few minutes until the potatoes are well-coated with the turmeric and oil. Add salt, mix in the coriander leaves, and set aside to cool.
Roll out the puff pastry into a square of about 8 inches. Cut with a pizza cutter into six pieces by making one cut down the middle and then three cuts horizontally.
Take one of the squares and roll separately into a slightly larger square. Place a couple of heaped teaspoons of the filling in the center, moisten two sides, and fold over the puff pastry in a triangle. Press down on the edges to ensure they are sealed.
Repeat until you have 12 puffs.
Bake in a 350-degree oven for 45-60 minutes on an ungreased baking sheet until they are crisp and lightly golden-brown.
Serve hot with some chutney or even ketchup.