Prepare the Shoestring Fries: Peel the russet potatoes and cut them into thin strips to create shoestring fries. Place the cut potatoes in a bowl of cold water and soak for at least 30 minutes to remove excess starch. This helps in achieving crispiness. Drain and pat the potatoes dry with a clean kitchen towel.

Fry the Potatoes: In a deep skillet or fryer, heat vegetable oil to 350°F (175°C). Carefully add the dried potato strips in batches, frying for about 3-5 minutes or until golden brown and crispy. Avoid overcrowding the pan. Use a slotted spoon to remove the fries and transfer them to a paper towel-lined plate. Sprinkle with salt immediately.

Cook the Ribeye Steaks: Season the ribeye steaks generously with salt and freshly ground black pepper on both sides. In a large skillet, heat a tablespoon of oil over medium-high heat. Once hot, add the steaks. Sear the steaks for about 4-5 minutes on each side for medium-rare, adjusting the time for your preferred doneness. In the last minute of cooking, add butter, crushed garlic, and thyme to the skillet. Baste the steaks with the melted butter using a spoon for extra flavor.

Make the Mushroom Gravy Sauce: In a separate saucepan, melt 2 tablespoons of butter over medium heat. Add the sliced mushrooms and sauté until they are tender and browned, about 5 minutes. Stir in the flour and cook for another minute to form a roux. Gradually whisk in the beef broth and Worcestershire sauce. Bring to a simmer and cook until the sauce thickens, about 3-4 minutes. Season with salt and pepper to taste.

Serve: Place the butter-basted ribeye steaks on a plate alongside a generous portion of crispy shoestring fries. Spoon the silky mushroom gravy sauce over the steaks and serve immediately.