For the quail, place the chicken stock, thyme and garlic into a pan over a medium heat and bring to a simmer.
Add the quail and simmer for 2-3 minutes.
Remove the quail with a slotted spoon and drain onto kitchen paper. When cool enough to handle, using a sharp knife, carefully cut the quail breasts away from the bone in one piece.
Heat a frying pan until hot and then add the oil and butter. Once the butter has is foaming, add the quail breasts skin-side down and fry for 3-5 minutes, or until there is moderate resistance when the thickest part of the breast is squeezed (or until completely cooked through).
Remove the breasts from the pan and leave to rest in a warm place for five minutes.
For the quail vinaigrette, heat a medium pan over a moderate heat. Add the vegetable oil and shallots and fry for one minute.
Add the quail legs and fry until golden-brown all over.
Add the thyme and rosemary and enough chicken stock to cover the quail legs completely. Bring to the boil, then reduce the heat and simmer for 20 minutes.
Strain the stock through a sieve and return to the pan (discard the solids). Return the stock to the boil and cook to reduce the liquid to a thick consistency, or until there is about 75ml/3fl oz remaining in the pan.
Add the olive oil and vinegar and whisk well, seasoning, to taste, with salt and black pepper.
For the spring onions, place the butter, garlic and bay leaf into a clean medium pan over a moderate heat.
When the butter has melted and is foaming, add the spring onions and fry over a very gentle heat for three minutes.
Add the two tablespoons of chicken stock and cook for a further five minutes, or until the spring onions are still a little al dente.
Remove the garlic and bay leaf.
For the watermelon, place the watermelon into a clean bowl with a little olive oil and a little freshly ground black pepper.
To serve, place three spoonfuls of the spring onions onto each plate. Top each with a quail breast and sprinkle some of the chopped cobnuts over each breast.
Arrange the watermelon cubes around the plate and spoon the quail vinaigrette over the quail breasts.