Probably should have taken a cross section but it was a bit cooked through (around med-well). Should have probably went hotter and shorter to get a rarer doneness but I'm not a chef
I suspected, and I'll be honest, I don't think slight deviation in either direction from medium would've made a big difference in tenderness for eye round. Medium-rare eye round is extremely chewy, unpleasantly so; a medium-well toughness is almost preferable.
Plus with steaks that thin, it's really impossible to get a good sear without a ripping hot charcoal grill or industrial kitchen equipment. Without either of those, the closest you can get is a screaming-hot cast iron pan with a touch of neutral, high smoke point oil that is just nearly beginning to smoke, so it
will fill your house with smoke if you can't cook outdoors or ventilate your kitchen well. When they're
almost done cooking, transfer to an ordinary pan over much lower heat for the butter and herb baste, as you don't want to burn those, nor continue cooking the steaks much further.
If you can't cook outdoors or fill your home with smoke, you're forced to use lower heat; cast iron is still ideal because it holds a lot of heat, but you'll have to stay well below the smoke point of beef fat and/or whatever oil you're using. In a home kitchen you have to compromise between trying to get some kind of sear on the outside without overcooking it, and on steaks that thin it's basically impossible. Cooking them straight from frozen could actually be your best strategy, as crazy as it sounds. It means you can't really season until after they're cooked, and I like to give steaks a short dry-brine in the fridge first, but for steaks that thin it also won't matter as much if there's not really much salt penetration.
