Preheat oven to 350°F/180°C. Line a baking sheet with parchment. In a medium bowl, mix together the flours, salt, baking powder and soda. Set aside.
In a large bowl, cream butter with sugars until light and fluffy. Add eggs one at a time and mix in thoroughly. Incorporate the vanilla.
Gently mix in the flour mixture, followed by the oats, and at last the chocolate chips and walnuts (if using). Keep aside some chocolate chips to top the cookies.
Add a couple of tablespoons of milk, if (and only if) the mix appears too dry. Drop the batter in 1-2 tablespoonfuls on your cookie sheet, at least 1" apart as they will spread while baking.
Bake for about 12-14 minutes or until browning at the edges.
Transfer cookies to a rack to cool and store in airtight containers at once or the cookies will soften.