Season the ribeye generously with salt, pepper, and garlic powder. Let rest at room temperature for 30 minutes.

Make the béarnaise reduction: combine red wine vinegar, minced shallot, black pepper, and half the tarragon in a small saucepan. Simmer over medium heat for 5 to 7 minutes until reduced to about 2 tablespoons. Let cool slightly.

Create a double boiler with a metal bowl over simmering water. Whisk the reduction with a splash of water and the egg yolks for 7 to 10 minutes until thick and frothy.

Gradually add melted butter one tablespoon at a time, whisking constantly to emulsify. Remove from heat and stir in lemon juice, remaining tarragon, and salt to taste.

Peel and cut potatoes into 1/4-inch sticks. Soak in cold water for 30 minutes, then drain and pat dry. Heat oil to 300°F and fry in batches for 6 minutes. Drain on paper towels.

Increase oil to 380°F and fry the potatoes a second time for 5 minutes until golden and crispy. Toss with Parmesan.

Heat a cast-iron skillet over medium-high heat until smoking. Sear the steak for 3 to 4 minutes per side. In the final 2 minutes, add butter, rosemary, and garlic, basting the steak with the foaming butter. Rest for 10 minutes, then slice against the grain and serve with frites and béarnaise.