Peel and halve the carrot lengthways, then peel and thinly slice the onions.
Take both legs off the birds and snap off the back bone at the base of the breastbone (or get your butcher to prepare them for you).
Place a shallow, heavy-based casserole dish over a medium–high heat, add 50g butter and brown the legs, skin-side down. Flip and repeat on the other side.
When they are brown all over, remove from the pan, add the carrot and onion, reduce the heat to low, pop on the lid and cook slowly for 30 minutes, stirring occasionally.
Add the vinegar and wine, then reduce by half. Return the legs to the pan, skin-side up. Add the thyme and pour over the stock to almost cover. Bring to a simmer, pop on the lid and cook in the oven for 1½ hours, until you can pull the meat from the bone.
Leave the dish in the oven but take off the lid so that the skin on the legs colours and crisps up, then remove from the oven, season and keep warm. Reduce the oven to 100ºC/gas ¼.
Place a heavy-based frying pan over a medium–high heat and colour the crown on all sides.
Add the remaining butter, reduce the heat and continuously baste the birds. Once they’re golden and crispy, cook in the oven until the temperature in the thickest part of the breast reaches 59ºC. Carve and serve with seasonal veg.