Prepare the fries: Place the cut potatoes in a large bowl and cover with cold water. Let them soak for at least 30 minutes, then drain and pat them completely dry with paper towels.
First Fry (Blanching): Heat the frying oil in a deep, heavy-bottomed pot or deep fryer to 300°F (150°C). Fry the potatoes in small batches for 5 to 7 minutes until they are pale and soft but not browned. Remove with a spider strainer and drain on a wire rack lined with paper towels. Let cool completely, at least 20 minutes.
Make the Herb Butter: In a small bowl, combine the softened butter, minced garlic, chopped parsley, and thyme. Mix well until incorporated. Set aside.
Remove the bowl from the heat. Slowly drizzle in the warm clarified butter while whisking vigorously until the sauce emulsifies and thickens. Stir in the chopped tarragon and cayenne pepper. Keep warm, but do not reheat directly.
Season the Steaks: Pat the steaks dry. Season generously on all sides with coarse salt and black pepper.
Second Fry (Crisping): Increase the oil temperature to 375°F (190°C). Fry the blanched potatoes in batches again for 2 to 4 minutes until they are deep golden brown and crispy. Remove and drain immediately. Toss lightly with salt.
Sear the Steak: Heat the olive oil in a heavy skillet (cast iron is best) over medium-high heat until shimmering. Place the steaks in the hot skillet. Sear for 3 to 4 minutes per side for medium-rare, pressing down lightly to ensure full contact.
Rest the Steak: Remove the steaks from the skillet and place them on a cutting board. Top each steak with a generous slice of the prepared herb butter. Let the steaks rest for 10 minutes before slicing.