Peel and cut the russet potatoes into thick fries. Soak the cut fries in cold water for at least 30 minutes to remove excess starch. Drain and pat them dry with paper towels.

In a large pot, heat vegetable oil over medium heat to 325°F (160°C). Fry the potatoes in batches for about 4-5 minutes until they are soft but not browned. Remove and drain on paper towels. Allow them to cool completely.

While the fries are cooling, season the flat iron steaks with smoked paprika, dried oregano, salt, and black pepper on both sides.

In a large skillet, heat olive oil over medium-high heat. Add the seasoned steaks and cook for about 4-5 minutes on each side for medium-rare, or until desired doneness is reached. Add butter to the skillet in the last minute of cooking and baste the steaks with the melted butter. Remove the steaks from the skillet and let them rest for 5 minutes.

In the same skillet, add the sliced mushrooms and sauté until they are golden brown, about 5 minutes. Add minced garlic and cook for an additional minute until fragrant. Stir in heavy cream, Dijon mustard, Worcestershire sauce, salt, and pepper. Simmer for 5-7 minutes until the sauce thickens slightly. Adjust seasoning to taste.

Increase the oil temperature to 375°F (190°C). Fry the pre-cooked fries again in batches for 2-3 minutes until they are golden brown and crispy. Drain on paper towels and season with salt.

Slice the rested steaks against the grain and serve with the creamy mushroom sauce drizzled over the top. Accompany with double-fried fries and garnish with fresh parsley.