Reserve the goat separately from the sauce. Strain the sauce and let the goat cool. When the goat is cool enough to work with, cut the meat off the bone and slice it into pieces that are a little larger than bite size.
If serving the goat right away, degrease the sauce by repeatedly dipping a large spoon or ladle just beneath its surface until the spoon fills with mostly clear fat; discard the fat. If you are cooking the goat ahead of serving it -- it can be prepared a day or two ahead up to this point -- refrigerate the goat and the strained sauce separately (moisten the meat with a little of the sauce). Before reheating, remove any hardened fat on top of the sauce.
Cook the degreased sauce at a rapid simmer until reduced by a third. (The sauce will be thin but very gelatinous. Too much reduction and the sauce will become sticky and unappealing.)
Reheat the meat in the sauce in a low (225 degree F) oven until heated through.
To cook the vegetables:
Heat 2 tablespoons vegetable oil in a large saute pan over medium-heat. Cook the potatoes until crispy and lightly browned. A few minutes into the cooking, add the shallots and peas so that they cook together. Season with salt and pepper; sprinkle with the chopped parsley.
Heap the potatoes and peas to one side of the plate. Lay the slices of goat near them and top with the sauce.