Chicken schnitzel: first, you need to butterfly your chicken breast until it's in two pieces. Butterflying cuts the chicken breast parallel with your cutting board so that you will have a flat, thinner piece of chicken. Here's a short butterflying tutorial if you've never butterflied a chicken breast before. After you've butterflied the chicken, go ahead and cut the large chicken piece in half so that you have two thin cutlets.
Cover the cutlets with plastic wrap or even better, a large zip-top bag that you have laid on top of the chicken. Using a meat mallet or a heavy pot, pound the chicken through the plastic to attempt to flatten each piece of chicken until it is less than 1/4-inch thick. This might take some effort and it will expand the width of your chicken piece considerably. After the chicken has all been pounded, cut each cutlet into pieces that are around the size and shape of your bread. You should be able to get 3 to 4 bread-sized, quarter-inch thick cutlets out of one chicken breast.
Set up your chicken dredging station. You will need three bowls or large plates for this.
The first bowl will contain all-purpose flour. Add 1/2 teaspoon salt and 1/2 teaspoon black pepper to the flour. The second bowl will contain 2 whole eggs whisked well. The third bowl will have breadcrumbs, 1 teaspoon salt, and 1/2 teaspoon black pepper. whisk to combine.
Add 1 to 2 inches of peanut or vegetable oil to a large pan or pot over medium-high heat and allow it to warm up until it's around 350 F (175 C).
Once the oil is up to temperature, carefully place each of your cutlets into the oil and fry them for 2 minutes, and then flip and fry for an additional 2 minutes. The cutlets should be very thin so they will cook quickly.
When the cutlets are fully cooked, remove them from the oil to a paper-towel-lined sheet pan or onto a cooling rack over a paper-towel-lined sheet pan.
Allow the cutlets to rest and cool for 5 minutes while you gather the ingredients to assemble your sandwich.
Sandwich assembly: grab two slices of bread and apply mayonnaise to one side of each piece (if using).
Top the mayonnaise with two to four of your chicken cutlets. If you're making two sandwiches, use half of your cutlets on each sandwich.
Top the cutlets with iceberg lettuce, tomato slices, and the second slice of bread. Serve and enjoy.