In a small bowl, combine smoked paprika, oregano, garlic powder, onion powder, salt, and black pepper. Rub the spice mixture all over the flat iron steak, ensuring an even coat. Let the steak marinate for at least 30 minutes at room temperature or up to 2 hours in the refrigerator for enhanced flavor.

Preheat your grill or grill pan over medium-high heat.

Once the grill is hot, drizzle olive oil over the grill grates to prevent sticking. Place the marinated steak on the grill and cook for about 4-5 minutes on each side for medium-rare, or until desired doneness is achieved. Use a meat thermometer to check for an internal temperature of 130°F for medium-rare. Remove the steak from the grill and let it rest for 5-10 minutes.

While the steak is resting, prepare the aioli. In a small bowl, combine the saffron threads with 1 tablespoon of warm water to bloom the saffron. In another bowl, whisk together the egg yolk, Dijon mustard, and lemon juice until well combined. Gradually drizzle in the olive oil while whisking continuously until the mixture thickens and emulsifies. Stir in the saffron mixture and then fold in the mayonnaise until smooth. Season with salt to taste.

Slice the rested steak against the grain into strips. Arrange on a serving platter and drizzle the saffron-infused aioli over the top or serve it on the side for dipping. Garnish with fresh parsley.