In a small bowl, combine the softened butter, mashed black garlic, parsley, chives, thyme, and lemon juice. Mix until well combined. Season with salt and pepper to taste. Transfer the mixture to a piece of plastic wrap, shape it into a log, and refrigerate until firm, about 30 minutes.

Take the New York strip steaks out of the refrigerator and let them sit at room temperature for about 30 minutes. Pat them dry with paper towels. Season both sides generously with salt, black pepper, and the cracked Szechuan peppercorns.

Preheat a grill or grill pan over medium-high heat. Cut the leeks in half lengthwise and brush them lightly with olive oil. Place the leeks cut-side down on the grill and cook for 4-5 minutes until charred and tender. Remove from the grill and set aside.

In a cast-iron skillet or a heavy-bottomed pan, heat 2 tablespoons of olive oil over high heat until shimmering. Add the seasoned steaks and sear for 4-5 minutes on each side for medium-rare, or until your desired doneness is reached. During the last minute of cooking, add a slice of the black garlic herb butter on top of each steak to melt.

Remove the steaks from the skillet and let them rest on a cutting board for about 5-10 minutes. Slice the steaks against the grain. Serve the steaks alongside the charred leeks and top with additional slices of the black garlic herb butter.