Heat the oil in a small saucepan over medium-high heat. Dredge the leek strips in arrowroot. Fry in the oil until lightly brown and crispy. Drain on paper towels and season with salt. Set aside.
Bring the white wine and vinegar to a boil in a medium saucepan. Add the shallots, salt and pepper, lower to a simmer and cook until most of the liquid is reduced. Turn the heat to low and whisk in 1 chunk of butter at a time, allowing each piece to melt before adding another. Remove from the heat, adjust the seasoning and strain through a fine sieve into a small bowl. Add the lemon zest. Place the bowl over warm water until ready to use.
Season the scallops on both sides with salt and white pepper. Heat a heavy-bottomed sauté pan over medium-high heat until hot. Add the ghee and swirl to coat the bottom of the pan. Once the ghee starts to sizzle, add the scallops one at a time, adjusting the heat to keep the scallops from burning. Once the scallops are well browned (1½-2 minutes) turn them over one at a time, in the same order they were placed in the pan. Cook 30 seconds to 1½ minutes longer, depending upon the size of the scallops.
Serve the scallops over the beurre blanc sauce and garnish with crispy leeks and steamed asparagus tips.