In a Dutch oven, heat oil until hot. Sear pheasant thighs in batches, gaining color on both sides but not attempting to cook through.
When the last batch is removed, add onion slices and cook until translucent, about 3 to 5 minutes. Add the garlic, smoked paprika, and cumin and cook one more minute to slightly toast the spices.
Deglaze hot pan by pouring in 1 cup of beef broth and scraping up all the flavorful bits stuck to the bottom of the pan.
Add the pheasant thighs back to the pan and add enough broth to cover the meat. Bring to a simmer and cover. Place in a 300-degree oven and braise for three hours.
After three hours, remove the pan from the oven and allow to cool completely. Remove pheasant thighs from the broth and shred. Set aside.
Strain the remaining liquid from the pan, setting aside the onions and garlic. Cook down the broth until reduced by half. In a blender, blend the onion and garlic mixture until smooth and this add back to the reduced broth.
Take one part of the reduction and one part prepared barbecue sauce and simmer together with a splash of orange juice. Season to taste.
For the Slaw: Combine ingredients and chill until ready to use.
Pour warm sauce over the shredded meat to lightly coat. Serve on toasted Hawaiian buns topped with honey-lime slaw and a dill pickle
