Thinly cut the chicken breast in half or pound it with a meat mallet or rolling pin to about half inch thickness.
In a small bowl, whisk one egg.
In a gallon-size Ziploc bag, add flour.
In a second gallon-size Ziploc bag, add bread crumbs.
Put 1 chicken breast in the flour bag, close and shake it up.
Dunk the chicken in the egg, coating completely.
Put the chicken in the breadcrumb bag and shake it up.
Repeat with remaining chicken breasts.
Add a tablespoon of olive oil to a medium skillet and let the oil heat up on medium heat. Then add chicken to pan. Allow each side to brown/crisp completely, being careful not to let the breading burn. Once the breading is browned (about 5-7 minutes), remove from pan (the chicken will continue cooking in the oven).
In a medium bowl, mix together ranch, ¼ cup shredded parmesan cheese and the grated parmesan cheese. You want the consistency to be thick enough that the mixture won't run off the chicken. Add more grated parmesan if the mixture is too runny.
Divide ranch mixture and spoon on top of breaded chicken.
Bake for 10 minutes.
Remove from oven and sprinkle with remaining shredded parmesan.
Bake for 5 additional minutes or until parmesan is browned and chicken is cooked to an internal temperature of 165.
Notes
You can also bake this chicken thoroughly, instead of pan-frying. Bake for 22-25 minutes in that case (adding parmesan at the last 5 minutes).