Preheat oven to 350F (for larger cookies) or 375F (for smaller cookies)
Cream butter with granulated sugar and brown sugar until light and fluffy.
Beat in eggs, 1 at a time. Stir in vanilla extract.
Sift flour with baking powder, salt and baking soda. Stir into butter mixture.
Add oats, cornflakes, coconut, chocolate chips and nuts and stir until blended.
Drop by tablespoons onto ungreased baking sheet. Flatten to 4-inch diameter. (Use square of wax paper to keep dough from sticking to fingers or whatever you're using to flatten dough.) For small cookies, drop by rounded teaspoon. Do not flatten.
Bake larger cookies at 350 degrees F for 10 to 12 minutes. Cookies should be slightly soft when removed from oven. Bake smaller cookies at 375 degrees F for 8 to 10 minutes.