Heat the oven to 200ºC. Place the beetroot, dukkah and a little olive oil in a small roasting pan, cover with foil and roast, covered, for 30 minutes, then a further 10 minutes uncovered. Remove and set aside.
Brush steak with olive oil and season with salt and pepper. Heat a pan until smoking hot, cook steak for 2–3 minutes on each side. Remove and set aside for 10 minutes before slicing into strips.
Whisk together all the dressing ingredients.
Place the steak on a platter, top with beetroot, feta cheese and baby red spinach leaves, drizzle over dressing. Serve with toasted pita bread.