Preheat a 12-inch cast iron skillet over medium-high heat until very hot, about 450°F; add the avocado oil and heat until it is just barely smoking.
Pat the ribeye steaks dry with paper towels and season both sides evenly with the kosher salt and black pepper.
Set a timer for 5 minutes, then add one steak to the hot skillet; flip the steak every 20–30 seconds for the full 5 minutes to develop an even crust.
With about 1 minute remaining, add 1 tablespoon of the compound butter to the pan and spoon the melted butter over the steak continuously.
When the 5 minutes are up, remove the steak from the skillet and tent loosely with aluminum foil; let rest for 10 minutes before slicing.
Repeat the cooking process for the second steak and serve with additional compound butter if desired.