Step #1 Heat oil in small saucepan; deep-fry thyme briefly, only about 5 seconds til fragrant.
Step #2 Remove thyme from oila & drain on absorbent paper.
Step #3 Prehead oven to moderate.
Step #4 Cut potatoes into 1cm slices; heat 2 tbsps of the reserved thyme oil in ovenproof/flameproof baking dish; cook potato slices in batches til lightly browned on both sides.
Step #5 Return all potatoes to baking dish; add lamb & roast, uncovered for about 15 mins or unil cooked as desired.
Step #6 Meanwhile, make aioli.
Step #7 Boil, steam or microwave spinach til just wilted; drain.
Step #8 Heat remaining thyme oil with butter in small saucepan; cook mushrooms & garlic til softened.
Step #9 Cut each lamb rack into 4 cutlets; divide among serving plates with spinach, potato & mushrooms.
Step #10 Top with aioli, garnish with fried thyme & drizzle with vinegar.
Step #11 Aioli: whisk mustard, vinegar, steady stream, whisking constantly, garlic & egg yolks in a small bowl til mixd; slowly add oil in a thin, til aioli thickens.