Season the beef. 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 under a preheated hot grill for about 5 minutes, shaking the pan frequently, until they are crispy. Set aside to cool.
Meanwhile, make the dressing by combining all the ingredients.
Thinly slice the beef and arrange it on the spinach leaves. Spoon over the dressing just before serving with the tortilla wedges.