To make the cabrito: preheat the oven to 300F. Season the meat evenly on all sides with salt, pepper and cayenne. Heat the olive oil in a Dutch oven set over medium-high heat. Sear the meat to a nice brown on all sides and remove.
Add the onions to the pot and sauté until translucent, about 8 minutes. Add the garlic, celery and carrots and sauté for 10 more minutes. Place the cabrito on the bed of vegetables and add the remaining ingredients.
Bring to a simmer, cover, and braise in the oven for 3 hours. When finished the cabrito should be tender. Remove from the pan and strain and reserve the liquid. When cool enough to handle shred the meat from the bone. Reserve.
To make the sauce: place all the ingredients in a heavy bottomed pot and warm slowly on a low burner for 30 minutes making sure garlic is soft. Add the cabrito, toss well and keep warm.
While the cabrito braises, make the pickles. Place cucumber the slices and onions in a large bowl and sprinkle with salt. Let sit for 10 minutes. Add the vinegar and 1/2 cup water and let stand for 3 hours.
Spoon small amounts of cabrito on small split slider buns and top with pickles.