Before you start, preheat oven to 230°C (or 210°C fan bake). Bring a large pot of salted water to the boil.
Prep potatoes and cook in pot of boiling water for 12 minutes until just beginning to soften. Drain well and allow potatoes to dry out in a colander.
Transfer dried potatoes to a lined oven tray and toss well with oil. Spread out in even layer and season with salt and pepper. Roast on upper oven rack for 25-30 minutes, until golden and crispy.
Prep tomatoes and basil and toss in a medium bowl with oil. Season with salt and pepper.
Heat oil in a medium fry-pan on medium-high heat. Cook lamb, fat side down, for about 2 minutes. Flip and cook for a further 1 minute, until golden. Transfer lamb to a lined oven tray and reserve pan. Cook lamb on lower oven rack, for 12-15 minutes, for medium-rare, or until cooked to your liking. Rest lamb covered for 5 minutes.
Heat butter in reserved pan on medium-high heat. Cook beans and almonds for 3-4 minutes, until beans are just tender and almonds are toasted.
Once rested, carefully slice lamb rack into cutlets by slicing down between upright bones.
Serve lamb with potatoes, beans, salad and Hollandaise.