In an 8- to 10-inch nonstick frying pan over medium-high heat, stir nuts often until golden, 3 to 4 minutes. Add currants, stir, and pour mixture into a small bowl.
In a wide bowl, mix 2 tablespoons oil and the vinegar. Add arugula leaves and mix to coat. Mound equal portions on salad plates.
Pour 1 tablespoon oil into the frying pan and set over medium-high heat. Lay cheese in pan and heat just until warm, turning once with a wide spatula, 3/4 to 1 minute total. Set a portion of cheese on each salad. Sprinkle with nuts and currants. Season to taste with salt and pepper.