Soak the dal in water to cover by 2 inches, and drain. Then make the filling: In a food processor or a blender, process the dal to make a coarse paste. In a spice or a coffee grinder, coarsely grind together all the whole spices (fennel to cardamom).
Heat 1⁄4 cup of the vegetable oil in a large nonstick kadai or saucepan over medium-high heat and add the asafoetida, then the ground spices, and stir about 30 seconds. Mix in the chickpea flour and stir another 30 seconds.
Add the dal paste and cook over medium heat, stirring and breaking any lumps, about 10 minutes. Add the salt and stir to mix well. Let cool and divide equally into 30 portions (about 1 tablespoon each). Make a ball of each portion and set aside. If the balls seem to fall apart, this means the filling is too dry; moisten it with 1 to 2 tablespoons hot water.
Make the dough: In a medium bowl, using clean fingers, rub together the flour, turmeric, and the remaining 1⁄4 cup oil until well mixed. Add enough water to make a soft and pliable dough, adding a little at a time. Place the dough on a cutting board and pound lightly with a meat mallet about 2 minutes. Turn the dough over during the 2 minutes to pound different sections. This makes the dough very elastic. Divide the dough equally into 30 portions.
Lift the edges over the filling, bring them together and pinch to seal. Then gently push in the pinched edges down to make a slight depression in the center and to flatten the patty to 1-inch thick. Brush the entire kachauri lightly with the flour-water paste and set aside. Finish assembling all the kachauries. Cover with a clean, damp cotton kitchen towel and set aside.
Heat the oil in a kadai or skillet over medium-high heat until it reaches 300°F to 325°F on a frying thermometer, or when a small piece of the dough dropped into the hot oil rises to the top after 15 to 20 seconds.
Reduce the heat to medium and add the kachauries, adding as many as the kadai can hold at one time without crowding, and fry slowly, turning only once after the bottom is golden-brown, about 3 to 4 minutes. When the other side is golden-brown, about 3 to 4 minutes more, remove from the kadai with a slotted metal spatula and transfer to paper towels to drain.
Serve immediately, or let cool and refrigerate up to 15 days.