In a shallow dish, combine the steaks, 1 tablespoon olive oil, paprika, thyme, and a generous pinch of black pepper. Season the meat with the ingredients, then set it away to marinade.
Cook the potatoes for 20 minutes or until cooked in a pan of boiling water. Drain and cut in half.
In a large frying pan, heat the remaining 2 tsp oil and add the potatoes. Cook for 15-20 minutes, or until golden brown. For the last minute, add the garlic.
Heat a griddle pan or another frying pan until very hot. Cook the steaks for 3 minutes on each side if you want them rare, 4 minutes if you want them medium, or 5 minutes if you want them well done. Place on a warm platter, cover with foil and leave to rest for 10 minutes.
Meanwhile, in a large saucepan, combine the spinach and sherry, cover, and cook for 2-3 minutes over medium heat; drain and season.
Serve the spinach beside the steak, potatoes, and a drizzle of the cooking liquids.