Mix flour, salt, and ajwain in a large bowl.
Add oil to the mixture and rub the oil into the flour until a coarse flour forms.
Add half of the water to the dry ingredients and mix with your hands. Add the remaining water to the part of the bowl with dry flour. Lightly knead the dough for 1-2 minutes, adding an additional 1 tablespoon of water if there is unhydrated flour remaining in the bowl. The dough won’t be smooth but should not have dry flour on the exterior. Cover with a damp towel and allow the dough to rest for at least 30 minutes.
Once the dough has rested, divide the dough into 2 equal sections.
Take one section of the dough and roll into a large rectangle that is roughly ¼-inch thick or 6 inches by 12 inches.
Using a fork, prick the entire surface of the dough with holes to prevent the papdis from puffing. Cut the dough into 18 squares that are roughly 2 inches by 2 inches. Alternatively, you can use a cookie cutter to cut circles if you desire! Repeat with the remaining section. Cover papdi with a towel when not working with it to prevent it from drying out.
Heat a deep, heavy bottomed pot with at least 3 inches of oil to 350 F. Fry for 5-7 minutes or until the papdi are a light golden color, then place them on a wire rack.
Papdis can be stored in an airtight container with a paper towel for up to 3+ weeks.