Mix together 4 tablespoons (1/2 stick) softened butter with the minced garlic, the chopped herbs and the lemon zest. Form into a log and refrigerate.
Generously season the filets with salt and pepper, approximately 1 teaspoon of seasoning per side.
Preheat your oven to 400 degrees.
Heat the remainder 4 tablespoons butter (1/2 stick) and the olive oil in a cast iron skillet to a screaming hot temperature (not burn you house down hot, though). Sear the filets in the hot pan for about 2-3 minutes per side or until a nice brown crust has formed. Once they're down, don't move them around.
While the steak is searing, continue to spoon the residual butter in the pan on top of the meat while it's cooking. Once both sides are seared, carefully place the entire skillet with steak in the center of the preheated oven for about 6-8 minutes, depending upon how thick your steak is.
In the last minute of cooking, take the log of compound butter and slice a thick piece to place on top; set aside.
Your steak will be ready when it is approximately 135 degrees in the center, or when you push lightly on the top center of the steak and it gently and slowly bounces back. Watch carefully especially if your steaks are thinner. Top with reserved compound butter.