Remove the steak from the fridge. Pat dry and set aside at room temperature for 30 minutes.
Prepare the Avocado-Cherry Salsa:
In a bowl, combine the cherries, cilantro, lime juice, and jalapeño. Season with salt and pepper. Set aside.
Cook the Steak:
Pat the steak dry once more and season all over with salt and pepper. Heat the neutral frying oil in a skillet over high heat. Once very hot, add the steak and cook without moving for 3-5 minutes (depending on steak thickness and desired internal temperature). Flip and add 1 tablespoon butter to the skillet and cook an additional 3-5 minutes. Baste the steak with the butter as it melts.
Transfer the steak to a cutting board and cover loosely with foil. Rest for 10 minutes before slicing.
Prepare the Tomatoes:
Melt the remaining butter in the skillet and add the tomatoes. Cook briefly in the residual heat, for about 2-3 minutes. Transfer to a bowl and keep warm.
Prepare the Avocado:
While the steak rests, peel the avocado and remove the core. Dice.
Dress the Greens:
In a bowl, toss the arugula with the extra virgin olive oil and lime juice. Season with salt and pepper.
Finish the Salsa:
Right before serving, fold the avocado into the remaining salsa ingredients. Taste and season again to your preferences.
To Serve:
Divide the arugula between plates and arrange the sliced steak on top. Pile the avocado-cherry salsa on top and spoon the warm tomatoes around the steak. Spoon any extra tomato juice from the bowl on top of each salad. Enjoy!