Place the Italian breadcrumbs in a large shallow bowl or cake tin and set aside.
Lay each steak between sheets of parchment or plastic wrap and gently pound with a meat mallet to an even thickness of about 3/4 to 1 inch.
Season both sides of each steak with coarse salt and freshly cracked pepper.
Pour 1/3 cup olive oil into a large shallow bowl or cake tin; coat each seasoned steak lightly in the oil and let excess drip off.
Press each oiled steak into the prepared breadcrumbs, coating all sides and pressing crumbs onto the surface; transfer to a sheet tray or platter and repeat with remaining steaks.
In a large non-stick or heavy skillet, heat 1/4 cup olive oil and 1/4 cup avocado oil over medium heat until shimmering, about 90 seconds.
Add steaks to the hot oil without crowding and cook undisturbed for 3 to 3 1/2 minutes, until the bottom is well browned.
Flip each steak and cook 2 to 3 minutes more, or until an instant-read thermometer registers 120°–125°F for medium-rare, or your desired doneness.
Remove steaks to a resting rack or plate and let rest briefly, then serve as desired (plain, over arugula with lemon, or with sauce).