For the dressing: Add the cilantro, mint, parsley, olive oil, sherry vinegar, zaatar, jalapeno, lime juice and shallot to the the jar of a blender. Puree, scraping the sides as needed, until smooth with just a few small chunks remaining. Set aside or refrigerate for up to 3 days in advance.
For the steaks: Sprinkle the steaks all over with 1 teaspoon salt and a generous amount of pepper. Set aside.
Melt the butter in a large skillet over medium-high heat. Add the steaks and cook, flipping halfway through, until a nice golden crust has formed on both sides and the temperature register 125 degrees F (for medium-rare) on an instant-read thermometer, 7 to 8 minutes total. Transfer to a cutting board and let rest for 3 to 4 minutes.
Return the skillet to the heat and turn to medium. Add more butter to the skillet if it is dry and add the zaatar. Toast until fragrant, about 1 minute. Stir in the shallot and cook, stirring occasionally, until softened, 5 to 6 minutes. Add the peas and saute until tender but still crisp, 1 to 2 minutes. Transfer to a plate, leaving any remaining butter in the skillet.
Meanwhile, mix the arugula and spinach together and place on a platter. Sprinkle with the avocado, radishes, peas and shallots. Slice each steak into thick slices and place atop the salad. Drizzle with the chimichurri dressing and serve immediately with the remaining chimichurri on the side.