Slice each large chicken breast in half horizontally, then cut each half into strips so you have 8 pieces total; place on a cutting board and cover with plastic wrap.
Using a meat mallet or the bottom of a heavy pan, pound each piece through the plastic wrap to an even 1/4-inch thickness.
Arrange three shallow dishes: in dish one combine 1/2 cup all-purpose flour with about 1/2 teaspoon salt and 1/4 teaspoon black pepper; in dish two beat the 2 eggs; in dish three place 3/4 cup bread crumbs.
Working with one piece at a time, pierce a corner with a fork, dredge in the seasoned flour shaking off excess, dip both sides in the beaten eggs, then press into the breadcrumbs until well coated.
Heat a large non-stick skillet over medium and add about 3 tablespoons oil to generously coat the bottom; when hot, place chicken strips in the pan without crowding.
Sauté each piece 3–4 minutes per side until golden brown and cooked through (no pink inside); transfer cooked pieces to a plate lined with paper towels and repeat with remaining chicken, adding more oil if needed.