In a large bowl or container, combine the water, kosher salt, and brown sugar, stirring until dissolved. Submerge lamb steaks in the brine, cover, and refrigerate for 1–2 hours. Remove, rinse under cold water, and pat completely dry.

Heat the oven to 400°F (200°C). Place shallots on a small baking sheet, drizzle with extra virgin olive oil, and season with salt. Roast until soft and caramelized, 25-30 minutes.

Add the roasted shallots to a blender with white wine vinegar, Dijon mustard, lemon zest, lemon juice, honey, and extra virgin olive oil. Blend until smooth, then pass through a fine-mesh strainer into a bowl or squeeze bottle for a silky finish. Adjust seasoning with salt and ground black pepper.

In a food processor, pulse pistachios, salt, and ground black pepper until you have a coarse crumb. Transfer to a shallow dish.

Heat grill to medium-high. Pat the lamb dry and brush lightly with avocado oil. Press each steak into the pistachio mixture so all sides have a thin, even crust.

Toss the leeks with avocado oil and season with salt. Grill over medium-high heat until charred and tender, 4–5 minutes per side. Transfer to a serving platter.

Place the lamb on the grates and sear 3–4 minutes per side for medium-rare. Move to indirect heat if the pistachios brown too quickly and cook until the internal temperature reaches 130–135°F (54–57°C). Remove from heat and rest for 5 minutes.

Slice the rested lamb steaks against the grain and arrange over the charred leeks with a handful of fresh arugula. Drizzle generously with the roasted shallot vinaigrette and sprinkle with the remaining chopped pistachios and fresh chives. Serve immediately while warm.