Pick over the split peas, wash well and cook in about 3½ cups water for 10-15 minutes, until the peas can be squashed under the back of a wooden spoon. Drain well.
Grind the cooked peas or blend in a liquidizer along with garlic and green chilies.
Mix the cumin, turmeric with 1 tsp water and blend into the puree, which should be dry rather than sloppy.
Sift the flour into a bowl, make a well in the middle and add the butter, oil, baking powder and salt.
Combine the ingredients to make a dough, adding as little warm water as possible, about 3 tbsp. The dough should be soft but not sticky.
Pull off a small piece of dough and roll it into a ball on a lightly floured pastry board. Make a hollow in the ball and stuff in a spoonful of a split pea mix. Stretch the dough to cover the stuffing, then roll and flatten the ball to make a small pancake. Repeat with the rest of the dough.
Heat a flat pan without any fat or oil. Cook the puri in the hot pan for about 2 minutes each side, until speckled and puffy.