Preheat the grill to a hot setting.
Season the beef with salt and freshly ground black pepper. Heat a large frying pan and sear the beef over high heat until it is cooked but still pink. This will take about 2 minutes each side, depending on thickness. Set aside at room temperature.
Grill the tortillas for about 5 minutes, or until they are crispy. Set aside to cool.
Meanwhile, make the dressing by combining all the ingredients in a small bowl.
Thinly slice the beef and arrange it on the spinach leaves. Spoon over the dressing and serve with the warm tortilla wedges.