To make the chicken Kiev, combine the softened butter with the chopped garlic and parsley in a bowl and season with salt and pepper.
Using a sharp knife, create a pocket in the side of each chicken breast by cutting into it parallel to your cutting board without cutting all the way through and opening it out like a book. Divide the garlic butter between the four chicken breasts and close over the flap again to make sure the butter is encased in the chicken.
Place the flour in a shallow bowl or plate and season with salt and pepper. Crack the eggs into a second bowl or plate and whisk together with the milk. Place the breadcrumbs in a third shallow bowl or plate. To coat the chicken, first dip it into the seasoned flour. Shake off the excess, then dip it into the egg mixture, again shaking of any excess. Finally, roll the chicken in the breadcrumbs, pressing gently to make sure the chicken is entirely coated. Set aside.
Place the potatoes in a saucepan. Cover with water, then add the garlic and a pinch of salt. Bring to the boil, then reduce the heat and simmer for 18 to 20 minutes, until the potatoes are cooked through. Drain and place the potatoes and garlic on a baking tray while still warm. Gently crush the potatoes with a potato masher, then scatter over the lemon zest, rosemary and some salt and pepper. Drizzle over the melted butter and roast the in oven for 10 minutes, until they are slightly crisp on top.
To make the pea purée, melt the butter in a saucepan, then add the shallot, garlic and smoked paprika and cook for 20 seconds. Add the stock and bring to the boil, then add the peas and remove from the heat. Blitz the peas into a purée using a hand-held blender. Check the seasoning and add the crème fraîche, if using. Set aside and keep warm until needed.
At this stage, heat a large frying pan with a generous splash of oil over a low heat and line a baking tray with a sheet of non-stick baking paper. Pan-fry the chicken on both sides until golden brown. Transfer to the lined tray and pop into the oven for an additional 20 to 22 minutes, until the chicken is completely cooked through.
Serve the chicken Kiev with the crushed potatoes and some pea purée.