Place the whole garlic cloves into a small saucepan and cover with cold water. Heat the mixture until boiling, then reduce the heat and simmer for one minute and drain. Repeat the process two more times.
Place the cooked, drained garlic into the same saucepan, pour over the double cream and season, to taste, with salt and freshly ground black pepper. Bring the mixture to the boil, reduce the heat and simmer for 5-7 minutes, or until the garlic is tender and the volume of the liquid has reduced by one-third.
Blend the mixture in a blender or food processor to a smooth purée and pass the mixture through a sieve into a clean bowl. Season, to taste, with salt and freshly ground black pepper and set aside.
Heat the sliced garlic and milk in a saucepan until boiling and cook for 5-6 minutes. Drain the mixture through a sieve and discard the milk. Pat the garlic slices dry with kitchen paper.
Heat some vegetable oil in a deep fat fryer to 190C/374F. Alternatively, heat the oil in a deep heavy-based frying pan until a breadcrumb sizzles and turns golden-brown when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Fry the garlic slices for 30 seconds, or until golden-brown and crisp. Remove from the pan and set aside to drain on kitchen paper. Season, to taste, with salt and freshly ground black pepper.
Season the lamb fillets with salt and freshly ground black pepper. Heat a griddle pan until hot and fry the lamb fillets for 2-3 minutes on each side (for medium), or until cooked to your liking. Remove from the pan and set aside to rest for 2-3 minutes.
Meanwhile, mix the borlotti beans, olive oil, balsamic vinegar, thyme and parsley together in a bowl. Mix the lamb's lettuce, garlic leaves and extra virgin olive oil in a separate bowl and season, to taste, with salt and freshly ground black pepper.
To serve, warm the lamb gravy in a saucepan. Carve each lamb fillet, at an angle, into five slices and arrange, in a fan shape, in the centre of each of four serving plates. Place some of the lamb's lettuce on top.
Spoon the garlic puré in dots around the edge of the plate and spoon the borlotti bean mixture in between the garlic purée dots. Drizzle the lamb gravy around the edge of the plate and scatter over the garlic crisps.