Pat the beef eye of round steak dry
Season both sides with salt and pepper
Let the steak sit at room temperature for 20 to 30 minutes
Heat a skillet over medium-high heat
Add a small amount of oil to the skillet
Sear the steak for 2 to 4 minutes per side
Reduce heat to medium or medium-low
Cook until the internal temperature reaches 130°F to 135°F for medium-rare or 140°F for medium
Remove the steak from the pan
Let the steak rest for 5 to 10 minutes
Slice thinly against the grain
Serve immediately