Heat a large non-stick pan over medium heat. Leave the buns stuck together (if applicable). Slice the buns in half, leaving a sheet of tops and bottoms. Melt 1/2 of the butter in the pan, take the top sheet of the buns and place into the pan, cook until golden brown then remove and set aside. Do the same with the bottoms of the buns using the remaining butter. Set both aside.
Butterfly the chicken, cover it with plastic wrap, and gently pound it to about a 1/4 inch thick using a mallet or rolling pin. Season the chicken on both sides with salt and pepper. Coat well with egg then coat on both sides with the breadcrumbs, pressing down with your hands to pack the breadcrumbs on tight.
Preheat the oven broiler on low.
Heat the oil in a non-stick pan over medium heat.
Fry the chicken on both sides to an internal temperature of 160°F using a thermometer and until golden brown. Set aside on paper towels to drain excess grease.
Spoon some marinara sauce on the bottom sheet of slider buns. Layer with chicken, spread more sauce on the chicken, and top with cheese. Place under the broiler until the cheese is melted. Then place the top layer of slider buns on top and cut into portions.
Serve with chips and pickles.