Preheat oven to 375ºF (190ºC).
In large bowl, whisk together all-purpose flour, whole wheat flour, Cheddar cheese, sugar, green onions, baking soda, salt and pinch of cayenne pepper.
In small bowl, whisk together buttermilk and oil. Add to dry ingredients all at once; stir with fork until soft dough forms.
Turn out dough onto lightly floured surface. With floured hands, press dough into ball; knead lightly 10 times. Place on greased baking sheet; gently pat out dough into 6-inch (15 cm) circle.
With sharp knife, score large X on top of loaf.
Bake in oven for about 45 minutes or until golden and tester inserted in centre comes out clean.