Cut the steak against the grain of the meat, into ½ inch thick slices, and set aside.
Heat the olive oil with the garlic and rosemary in a heavy 12 inch skillet over medium heat. Stir the garlic often until it is golden brown, about 4 minutes.
Raise the heat to high and add the meat to the skillet. Sauté, stirring often, to brown evenly, about 3 minutes.
Add the arugula to the skillet, season with salt and pepper and sauté until barely wilted, for about another minute.