For the beurre noissette, heat two small saucepans and divide the butter between them. Add the lemon thyme to one saucepan and add the rosemary to the other, this will give you two different burnt butters. Cook until the butter turns golden brown, remove from the heat.
Preheat the oven to 220C/200C Fan/Gas 6.
For the turkey jus, heat a roasting tray in the oven and add the oil. Add the turkey meat and roast until golden brown and cooked through, stirring from time to time, this should take about 15 minutes. Remove the roasting tray from the oven and put on the hob over a medium-low heat.
Add the onion and garlic, flesh side-down, and cook gently until lightly coloured. Add the thyme and deglaze the roasting tray with 500ml/18fl oz water.
Transfer to a large saucepan and stir in the chicken stock. Bring to the boil, then reduce to a simmer and cook for 3 hours, skimming off any scum and excess fat. Strain in a colander and pass through a fine sieve, then put back in the pan and reduce to 500ml/18fl oz. Set aside.
For the Lyonnaise potatoes, melt 40g/1½oz butter in a heavy-based saucepan. Add the onion and thyme and season with salt and pepper. Cook, stirring from time to time, until soft and transparent.
Meanwhile heat the oil in a deep-fat fryer or a deep-sided, heavy-based pan to 140C, or until a breadcrumb sizzles and turns golden-brown when dropped into it. (CAUTION: hot oil can be dangerous. Do not over-fill the pan or leave if unattended). Blanch the potatoes in the oil until soft and lightly coloured. Drain on kitchen paper and leave to cool.
Heat the remaining 4 teaspoons oil in a frying pan with the remaining butter. Add the blanched potatoes and cook until golden brown. Drain away the excess butter, and add the cooked onion and the mustard to the potatoes. Mix well, then add the parsley and season with salt and pepper.
For the tomato concasse, half-fill a bowl with iced water. Remove the stalks from the tomatoes and cut away what remains of the stalk area. Using a sharp knife, cut across the top of each tomato. Plunge each tomato in boiling water for 10 seconds and refresh in the iced water. Peel the tomatoes, cut into quarters and remove the seeds. Cut the tomato quarters into strips, then into small dice.
To make a sauce for the lemon sole, take the thyme beurre noisette and strain through a sieve, add the turkey jus and simmer until it has reduced by two thirds, then season with salt and pepper and set aside.
For the lemon sole, preheat the oven to 200C/180C Fan/Gas 6. Season the fish with salt and pepper. Heat the remaining butter and a drop of oil in an ovenproof frying pan over a medium heat. Before the butter turns golden-brown add the fish thick side-down. Once the fish starts to colour, place the pan in the oven for 5 minutes, then turn the fish to cook for a further 4 minutes. Cook in batches if needed.
For the garnish, put your rosemary beurre noisette in a pan. Add the brown shrimp and heat gently. Add the lemon segments, baby capers, tomato concasse, shallots, parsley, and peas. Season with salt and pepper, keep warm.
Sprinkle the fish with lemon juice. Leave it to stand for 1 minute while you put some of the Lyonnaise potatoes in the middle of each serving plate. Put the fish on top of the potatoes and spoon the rosemary noisette garnish over it. Pour over the lemon sole sauce and serve.