Take the Porterhouse steaks out of the refrigerator and let them come to room temperature for about 30 minutes. Preheat your grill or a cast-iron skillet over medium-high heat.

In a small bowl, combine the olive oil, chopped rosemary, sea salt, and black pepper. Rub the mixture generously over both sides of the steaks.

Place the steaks on the grill or skillet and cook for about 4-5 minutes on each side for medium-rare, depending on your preferred doneness. Use a meat thermometer for best results (130°F for medium-rare). Once cooked, remove the steaks from the heat and let them rest for 5-10 minutes.

In a small saucepan over medium heat, combine the balsamic vinegar, chopped dried apricots, and honey. Bring to a simmer and reduce the heat to low. Allow the mixture to simmer for about 10-15 minutes, or until it thickens slightly. Stir in the unsalted butter until melted and well combined.

Slice the rested Porterhouse steaks and arrange them on a serving platter. Drizzle the balsamic-apricot reduction over the steaks and garnish with fresh rosemary sprigs.