Sift the flours into a large mixing bowl and add the cardamom and salt. Work in the buttermilk and 1 tablespoon of the oil to make a soft dough.
Knead on a lightly floured surface for 10 minutes and form into a ball. Cover with a damp cloth and leave to rest for 20 minutes.
Divide the dough into 12 balls and roll each one out into a 15 cm (6 inch) disc. Brush a paratha with a little oil, fold in half and then brush again. Fold in half again to form a triangle, dust with a little flour and flatten with a rolling pin to make a 15 cm (6 inch) triangle. Repeat with the remaining breads.
Heat a nonstick griddle pan or frying pan over a medium heat. Brush with a little oil and cook each paratha for 1 minute, pressing down with a spatula. Turn it over, brush with a little more oil and cook for a further 1 minute.
Remove each paratha and keep warm wrapped in foil while you cook the remaining breads. Serve warm with any curry of your choice.