In a food processor, process oats until fine. Add wholemeal and plain flours, sugar, bicarbonate of soda and ½ teaspoon salt. With motor running, add butter. Process until mixture resembles breadcrumbs. With motor still running, add eggwhites. Process until mixture forms a ball.
Divide mixture in half. Roll out each half between floured baking paper into 23cm circles. Place on prepared trays. Chill for 30 minutes.
Preheat oven to 200°C or 180°C fan. Cut each circle into eight wedges. Bake for 15 minutes. Cool. Serve biscuits with cheese.