In a mixing bowl, combine the toasted hazelnuts, dried tarragon, olive oil, salt, and black pepper. Mix until the hazelnuts are well coated.

Pat the strip steaks dry with paper towels. Season both sides generously with salt and black pepper.

Press the hazelnut mixture onto one side of each steak, ensuring an even coating.

Heat a large skillet or grill over medium-high heat. Once hot, add the steaks, crust side down. Cook for about 4-5 minutes until the crust is golden brown.

Flip the steaks and continue to cook for another 4-5 minutes for medium-rare, or until desired doneness. Use a meat thermometer for accuracy (130°F for medium-rare).

While the steaks are cooking, place the lemon halves cut-side down in the skillet or on the grill. Cook for about 2-3 minutes until charred and caramelized.

In a small saucepan, melt the butter over medium heat. Once melted, stir in the chopped capers and cook for 1-2 minutes until fragrant. Remove from heat.

Remove the steaks from the heat and let them rest for 5 minutes. This allows the juices to redistribute for a more tender steak.

Slice the steaks against the grain and serve with charred lemon halves on the side. Drizzle the caper butter over the top and garnish with fresh tarragon leaves if desired.