Beat butter, yogurt, brown sugar, and white sugar with an electric mixer in a large bowl until smooth. Add eggs one at a time. Beat in vanilla extract. Mix in flour and baking soda until just incorporated. Fold in quick oats, walnuts, chocolate chips, carrots, and cranberries. Roll dough into walnut-sized balls and place 2 inches apart onto ungreased baking sheets.
Bake in preheated oven until cookies are golden brown, about 12 minutes. Allow cookies to cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.