For the paloise sauce, melt the butter in a medium saucepan on a gentle heat. Skim the white foam that floats to the top off the butter. Then pour the butter into a clean bowl, leaving behind any milk solids that have sunk to the bottom of the pan. Add the bunch of mint to the butter.
Place the vinegar, white wine, peppercorns and shallot into a small saucepan and bring to the boil. Reduce the heat and simmer until the volume of the liquid has reduced by half.
Remove the peppercorns, and then pour the mixture into a medium heat-proof bowl. Allow to cool slightly.
Whisk the egg yolks into the white wine reduction.
Place the bowl over a pan of simmering water (ensure the bottom of the bowl does not touch the water) and whisk the eggs together until thickened and light in colour.
Strain the mint-flavoured butter through a sieve into the egg mixture, whisking constantly.
Season with salt and freshly ground black pepper, then add the lemon juice and chopped mint leaves.
Turn off the heat and leave the bowl over the pan until ready to use.
For the crushed new potatoes and green beans, place the potatoes in a medium saucepan and add cold water bring to the boil and cook for 10-15 minutes until the potatoes are cooked. Drain.
Bring a medium saucepan of water to the boil and add the beans. Boil for one minute, then drain.
Heat a small frying pan and add half the butter. Add the blanched beans to the pan and cook for a minute.
Crush the new potatoes slightly with a fork and add the remaining butter. Season with salt and pepper.
Pre-heat the oven to 200C/400F/Gas 6.
For the duo of lamb, heat a large frying pan and add the oil, season the fillets with salt and fry until browned all over. Transfer to the oven for 8-10 minutes. Remove from the oven and allow to rest.
Meanwhile, heat a griddle pan until hot. Brush the chops with oil and season with salt and freshly ground black pepper. Place on the griddle and cook for a couple of minutes on each side. Set aside to rest for a few minutes.
To serve, slice the lamb fillets and place onto a plate with a lamb chop, serve with the new potatoes, green beans alongside and sauce drizzled over.