Mash the softened butter with the parsley, chives, thyme, grated garlic, 1 tsp lemon zest, and flaky salt in a 20 cm / 8-inch bowl until evenly speckled. Spoon it onto parchment, roll into a log about 4 cm / 1.5 inches wide, twist the ends, and chill for 20 minutes until firm enough to slice.

Trim any fat cap thicker than 5 mm / 1/4 inch. Pat the steaks dry with paper towels, rub with 1 tsp of the avocado oil, and season both sides and the edges with the kosher salt and pepper. Leave them on a plate at room temperature for 30 minutes.

While the steaks sit, set up the grill for two-zone cooking, with coals banked to one side or only one side of the burners on high. Heat to about 230 C / 450 F for 10 to 15 minutes, then scrub the grates and wipe them with the remaining 1 tsp oil on a folded paper towel.

Pat the steaks dry again if moisture has beaded on the surface. Grill over direct heat with the lid closed for 4 to 5 minutes, flip once, and grill another 4 to 5 minutes, until an instant-read thermometer in the thickest part reads 130 F / 54 C. If fat drips and flames climb the steak, slide it to the cool zone until they die down, then move it back.

Move the steaks to a cutting board. Slice the herb butter into 1 cm / 1/2-inch coins, lay 2 coins on each steak, and rest for 5 minutes. Meanwhile, toss the arugula with 1 tbsp lemon juice, the olive oil, and a pinch of salt and pepper in a 30 cm / 12-inch bowl.

Slice the steaks against the grain into 1 cm / 1/2-inch strips. Pile the greens on two plates, lay the steak on top, and spoon over the melted butter and juices from the board. Serve right away.