Lightly season the chicken cutlets on both sides with salt and pepper.
In a low bowl, beat eggs to make an egg wash. Place your seasoned breadcrumbs in a second low bowl.
In a non-stick skillet with lid, melt butter and olive oil over high heat.
Dunk chicken pieces in egg wash, then breadcrumbs, making sure the pieces are evenly and thoroughly coated with crumbs.
Add chicken to hot butter/oil and cook until bottom is nicely browned (3-4 minutes). Turn down heat to medium-low and flip chicken over. Cover with lid, and cook until bottom of chicken is nicely browned (3-4 minutes).