Preheat the oven to 450 degrees . On a baking sheet, toss the potatoes with 2 tablespoons EVOO. Reserve 1 teaspoon each of rosemary and thyme and sprinkle the rest over the potatoes. Sprinkle with grill seasoning and roast for 25 minutes.
Season the steaks with grill seasoning. Preheat a grill or grill pan. Using a food processor, coarsely chop the olives and yellow onion. Transfer to a bowl. Mix in half the garlic, the reserved rosemary, the finely chopped red bell pepper and 1/3 cup EVOO. Set the olive sauce aside.
In a bowl, combine the remaining red bell pepper, the green bell pepper, chopped red onion, pickled peppers, remaining garlic, finely chopped tomato, reserved thyme, juice of 1/2 lime, red wine vinegar, 1/3 cup EVOO and salt and pepper to taste. Set the salsa aside.
Grill the steaks over direct heat for 3 minutes on each side, then over indirect heat for another 5 minutes for medium-rare. (Or grill in a grill pan over medium-high heat for 3 minutes on each side, then roast in a 350 degrees oven for 8 to 12 minutes for medium-rare.) Let the meat rest for 5 minutes.
While the steaks cook, place the tomato wedges in a bowl. Thinly slice the avocado and add to the tomato. Add the sliced red onion and hearts of palm. Add the arugula and toss the salad with the remaining lime juice, the remaining EVOO and salt and pepper to taste.
Top each steak with both sauces and serve with 3 potato wedges and some salad alongside.