Bring a large pot of lightly salted water to a boil. Turn off heat and stir in cabbage and carrots; let stand for 2 minutes then drain in a colander. Rinse well with cold water, then squeeze dry.
Place shredded cabbage and carrots into a large bowl along with the onion, oregano, and mayonnaise. Mix together until you have a mixture resembling coleslaw. This is the curtido.
To prepare sandwiches, lightly spread each roll with mayonnaise and pile with shredded turkey. Place a scoop of curtido on top of the turkey, and finish with sliced tomatoes, cucumbers, and radishes.