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For the peppers and onions: Heat the oil over high heat in a saute pan and sear the peppers and onions for 2 to 3 minutes. Stir in the tarragon and rosemary. Sprinkle in the vinegar and toss to coat. Season with salt and pepper.
For the salad and vinaigrette: Mix together the vinegar and red onions in a small stainless-steel bowl Pour the orange juice into a saucepan and cook until reduced to a syrup, and then let cool. Whisk the orange juice reduction and olive oil into the vinegar to create an emulsified vinaigrette. Add salt and pepper to taste.
For cooking the steaks: Heat 1/8 cup olive oil in a cast-iron skillet until it just begins to smoke. Lightly sprinkle the steaks with salt and pepper and sear over high heat on each side until medium rare, 34 minutes per side.
Combine the arugula, cherry tomatoes and vinaigrette in a bowl. Season with salt and pepper if necessary. Divide the salad among 46 dinner plates. Slice steak against the grain and place on the plates. Garnish with the peppers, onions and Cheddar.