Pat the chicken dry with a paper towel. Place the eggs and bread crumbs into two separate shallow dishes. Completely coat the chicken in the eggs, then the bread crumbs. Set aside on a clean plate.
Add the olive oil to a large skillet (I use nonstick) over medium heat. After a minute, drop a bit of bread crumbs into the oil to see if it sizzles. If not, wait another minute for the oil to heat.
Add the chicken, tilting the pan to move the oil around as needed, and being careful not to overlap the pieces. Cook for 3 minutes, then turn over and cook for 3-4 more minutes, or until the chicken registers 165 degrees F with an instant-read thermometer. If the bottom starts to brown too deeply, lower the heat slightly.
If all of your chicken doesn't fit in the pan at the same time without crowding, plan to do this in two batches—adding more oil in between. Add a slice of cheese to the top of each cutlet so it starts to melt.
Remove chicken from the pan with tongs, drain on a paper towel if desired. Make the salad.
To assemble the sandwiches: Add a thin layer of marinara sauce to the base of each roll. Add the chicken (with the cheese), then the salad. If the rolls are very thick, feel free to remove the inside of the top half of the roll so there is more space for the salad.
