Heat oven to 400° F. In a medium bowl, toss the potatoes with 2 tablespoons of the oil, 3/4 teaspoon of the salt, and 1/4 teaspoon of the pepper. Transfer to a rimmed baking sheet and roast, stirring once, until the potatoes are golden, about 25 minutes. Meanwhile, season the steaks with 3/4 teaspoon of the salt and 1/4 teaspoon of the pepper. Heat 1 tablespoon of the oil in a large skillet over medium heat. Cook the steaks to the desired doneness, about 4 minutes per side for medium-rare. Transfer to a cutting board, cover with foil, and let stand for 10 minutes.
Meanwhile, in a large bowl, whisk together the mustard, vinegar, and the remaining salt and pepper. Whisking constantly, slowly add the remaining oil and the tarragon. Toss the spinach with the vinaigrette, slice the steaks, and serve the salad and meat alongside the potatoes.
Tip: You can make this recipe with almost any steak; strip, flank, and skirt work just fine. For optimal tenderness, slice the meat across the grain.