Beat butter, white sugar, and brown sugar with an electric mixer in a large bowl until smooth. Add eggs, one at a time, allowing each egg to blend into the butter mixture before adding the next. Beat in vanilla extract. Combine all-purpose flour, whole wheat flour, baking soda, salt, and cinnamon in a separate bowl; stir into butter mixture. Fold in oats and dates. Cover and chill dough for at least one hour.
Preheat oven to 190 degrees C. Grease two baking sheets.
Roll dough into walnut-sized balls and place 2 inches apart onto baking sheets. Flatten each cookie with a large fork.
Bake in preheated oven until cookies are golden brown, 8 to 10 minutes. Allow cookies to cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.