Season pork with salt and pepper. Heat 1 teaspoon oil in a Dutch oven or heavy soup pot over high heat. Add pork and cook, stirring occasionally, until browned on all sides, about 6 minutes. Transfer to a plate lined with paper towels and set aside.
Reduce heat to medium and add remaining 1 teaspoon oil to pot. Add onion and bell pepper and cook, stirring, until vegetables are soft, about 5 minutes. Add garlic, curry powder, thyme, allspice and cinnamon; cook, stirring, until fragrant, about 1 minute more.
Add broth, sweet potatoes, tomatoes, chiles and bay leaf. Bring to a simmer, reduce heat to low. Cover and simmer, stirring occasionally, until sweet potatoes are very tender and the sauce has thickened, 15 to 20 minutes.
Add reserved pork and cook until heated through, about 3 minutes. Remove chiles and bay leaf. Adjust seasonings and serve.