Season chicken breasts with salt & pepper on both sides. Heat a large skillet over medium heat with 1 tbsp. olive oil. Place chicken in skillet and cook 5-6 minutes, then flip over and cook another 5-6 minutes until chicken reads at least 165 degrees in the middle.
When chicken is done, turn off heat and place a slice of cheddar cheese on each chicken breast. Allow chicken to sit in the pan for a few minutes to melt the cheese.
While cheese is melting, combine mayo & dried cranberries in a small bowl. Slice a granny smith apple into thin slices.
To assemble the sandwiches, spread layer of cranberry mayo on top side of brioche bun. Place chicken breast on bottom bun and top with apple slices. Top with cover bun and serve.