1-2 hours before cooking, sprinkle the goat liberally with salt, pepper, and a light (but thorough) dusting of sweet (dulce) smoked paprika. Place on a plate in the fridge. Remove the goat from the fridge about 30 minutes before cooking.
Preheat oven to 275˚F
Heat oil in a large dutch oven over medium-high until hot.
Brown the goat generously on all sides until very brown and remove from the pan.
Add the onion, garlic, celery, and carrots to the pan and sweat the vegetables on medium-low for about 5 minutes.
Add white wine and sherry vinegar and cook for 3 minutes.
Add chicken stock, return the goat shoulder to the pan and bring to a simmer. Cover and put the pot in the oven.
Cook the meat for 4-5 hours, or until tender, turning occasionally.
When tender, remove the meat from the braise, cover with foil and keep warm.
Strain the sauce into a saucepan and reduce the sauce on medium-high heat until just beginning to thicken.
You should end up with roughly ½ cup of liquid.
When pleased with the consistency of the sauce, (it should be pretty thick and definitely coat the back of a spoon) remove from heat and whisk in the butter.
When ready to serve, slice the goat and fan the slices on a pre-warmed plate.
Spoon the sauce over the meat and serve.