Take steaks out of the fridge to rest at room temp for 10 minutes. Season generously all over with salt and pepper.
Heat a cast iron skillet to medium-high until very hot and then add avocado oil. Transfer steaks to skillet and sear on both sides until crust forms, about 4 minutes per side.
Turn heat down to low and add the butter, garlic cloves and fresh herbs. Baste the steaks for a minute or two (steaks internal temp should be 130 F for medium rare) then transfer to a cutting board. Cover with foil and rest for at least 10 minutes. Slice against the grain into thin pieces.
Halve baguette and toast in the oven for 10 minutes at 350 F. You want a light toast on this, don’t let it get too brown or crispy.
Prepare arugula dressing by mixing together olive oil, lemon juice, minced garlic, salt and pepper in a large bowl. Add in the arugula and toss to coat. For the garlic mayo, mix together ingredients in a medium bowl (or use a store-bought version for a shortcut).
Spread both sides of toasted bread generously with garlic mayo. Top one side with thin slices of steak, desired amount of arugula salad and shaved parmesan. Then place the other piece of bread on top to enclose sandwich and cut in half before serving.