For the braised leeks: Cut the leek in half down the middle and then crosswise into 4-inch pieces.
Place a medium high-sided skillet over medium-high heat and add the butter to melt. Add the leeks to the pan, cut-side down, and brown for a couple minutes. Turn over, season with lemon zest, salt and pepper, and add the stock. Bring to a simmer and cook until the pan is dry and the leeks are tender, 20 minutes.
For the lamb chops: Preheat the oven to 425 degrees F.
Melt the butter in a small skillet over medium heat. Add the garlic and stir for a few seconds, then add the fine breadcrumbs, panko breadcrumbs and rosemary. Cook, stirring, until lightly toasted and fragrant, 2 minutes. Set aside.
Heat the olive oil in a small skillet over medium-high heat. Score the fat on the rack of lamb. Add the lamb to the skillet and sear until golden brown, 1 to 2 minutes per side. Let cool slightly and then slather all over with the Dijon. Top with the breadcrumb mixture, patting it to adhere. Place the lamb, fat side up, on a baking rack set over a baking sheet and transfer to the oven. Roast until medium (130 degrees F), about 8 minutes. Let rest for 10 minutes.
For the scallops with beurre blanc: Clean the scallops by removing and discarding the foot. Set aside.
Place a small saucepot over medium heat and add the white wine, white wine vinegar, lemon juice and shallot. Bring to a simmer and cook until reduced to a few tablespoons, 10 to 12 minutes. Turn the heat to low and whisk in the butter, piece by piece, until fully incorporated. When you get to the last piece, remove the pot from the heat, season with salt and white pepper, and whisk in the cream and add tarragon. Set aside until ready to use. If you need to reheat, place over very low heat.
Place a small skillet over medium-high heat; add some olive oil. Dry the cleaned scallops well with a paper towel, then season with salt. Sear the scallops until barely opaque throughout, 1 to 2 minutes per side. Remove from pan and let rest on a paper towel until ready to plate.
Plate the leeks and top with the lamb chops. Serve with the scallops on the side, drizzled with buerre blanc.