Preheat the oven to 375F. Begin by preparing the potatoes and sauce first. Place the baby potatoes into a large pot of salted water and bring to a boil. Cook the potatoes for approximately 15 minutes, until fork tender. Drain out the water and let them stand while preparing the rest of the recipe.
Preparing the Sauce:
Prepare the sauce next. In a small saucepan, combine all the sauce ingredients: soy sauce, water, rice vinegar, sugar, sesame seed oil, ginger and garlic. Whisk everything together, then bring to a simmer over medium heat. Simmer for 5 to 7 minutes, until the sauce is reduced in half.
Preparing the Lamb:
Meanwhile, prepare the lamb. Trim the rack of stiff, hard fat and french the tips, if desired. Section the rack into pairs of chops. Season the lamb all over generously with coarse sea salt. Preheat a large frying pan over medium-high heat and add a few tablespoons of olive oil. Once the oil is hot, reduce the heat to medium and add the lamb, fat side down first. Brown the lamb all over.
Once the lamb is well browned, add the prepared ginger garlic sauce. Allow the sauce to simmer for a minute, then transfer the pan into the preheated oven. Bake at 375F for 12 minutes, turning and braising once. Remove the lamb from the oven and allow it to rest for 10 minutes before slicing each pair of chops in half. Keep the lamb warm until serving.
Finishing the Potatoes:
While the lamb is in the oven and resting, finish preparing the potatoes. Add a few tablespoons of olive oil into the pot of potatoes and season with salt, pepper and seasonings. Close the pot with a lid and toss the potatoes until they are well coated. Transfer the potatoes into a large frying pan. Using a potato masher, crush the potatoes slightly, just enough to burst them open.
Cook the potatoes over medium heat, 4 to 5 minutes per side, turning just once to avoid breaking the potatoes apart. Once the lamb is rested, plate the lamb with the crushed potatoes and spoon additional garlic sauce over the lamb and potatoes.