Preheat an oven to 350 degrees F (175 degrees C). Pat pork roast dry with a clean towel. Mix curry powder, turmeric, garam masala, ground ginger, chili powder, cumin, cayenne, salt, and pepper in a small bowl. Rub spice mixture all over the pork roast.
Heat the olive oil and butter in a large, heavy bottom pot or Dutch oven over medium-high heat. Place the seasoned pork roast into the pot and cook until evenly browned, about 2 minutes on each side. Remove pork and set aside. Stir in the garlic and onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Stir in the fig compote, until well blended. Return pork to the pot, coating it with the fig mixture. Pour in the tomatoes and chicken broth. Cover, and bring to a boil.
Place covered pot in the preheated oven. Cook until the pork is no longer pink in the center, about 2 hours. An instant-read thermometer inserted into the center should read 145 degrees F (63 degrees C).