Pat the chicken dry with kitchen paper, lay on a wire rack and chill in the fridge uncovered, on the bottom shelf, overnight.
The following day, preheat the oven to 200C/180C Fan/Gas 6. Beat the softend butter and brioche crumbs together in a large bowl then add the leaves from 6–8 sprigs of the thyme. Season with plenty of salt and pepper then spoon the mixture into a piping bag. (Alternatively, spoon into a food bag then snip a corner off).
Carefully loosen the skin covering the chicken breasts and pipe the butter mixture between the skin and the breast meat. Smooth the skin down and season the chicken all over with sea salt. Stuff the cavity with the garlic, lemon and remaining thyme then lay in a roasting tin. Pour in a third of the stock, cover tightly with kitchen foil and roast for 1¾ hours.
At the end of the cooking time, increase the oven temperature to 220C/200C Fan/Gas 7. Remove the chicken from the oven and discard the foil. Brush the chicken generously with melted butter and return to the oven for 10–15 minutes, or until the skin is golden brown and crisp. Remove the chicken from the oven, transfer the chicken to a board and set aside to rest for 20 minutes.
Meanwhile, skim any excess fat from the cooking juices and set the roasting tin over a high heat. Whisk in the flour and cook for a couple of minutes, stirring occasionally. Pour in the remaining stock and stir, scraping up any sticky bits from the bottom of the tin. Simmer for 5 minutes then strain into a clean pan.