Preheat oven to 350°F.
In a large skillet, heat the vegetable oil over medium-high heat. Add the pork belly cubes and cook until browned on all sides, about 5 minutes.
Add the chopped onion and minced garlic to the skillet and cook until softened, about 3 minutes.
In a small bowl, whisk together the chicken broth, soy sauce, brown sugar, and black pepper. Pour the mixture over the pork belly and onions in the skillet.
Transfer the skillet to the preheated oven and bake for 1 hour, or until the pork belly is tender and the sauce has thickened.
While the pork belly is cooking, make the blueberry compote. In a small saucepan, combine the blueberries, honey, and balsamic vinegar. Cook over medium heat, stirring occasionally, until the blueberries have burst and the mixture has thickened, about 10 minutes.
Serve the braised pork belly with the blueberry compote on top.