Cut cooked pork belly into 1/2-inch cubes. Set aside.
Heat butter in a large skillet over medium heat until melted and sizzling; add beaten eggs and swirl into an even layer. When eggs are starting to set, gently cook and stir until scrambled. Transfer to a clean plate.
Add pork belly to same skillet; cook and stir with a spatula until all sides are crisp and golden brown, 4 to 5 minutes. With a slotted spoon, transfer to plate with eggs.
Pour off all but 2 tablespoons of fat from the skillet (or add oil or butter to equal 2 tablespoons) and increase heat to medium-high. Add onion; cook and stir until it begins to soften, 1 to 2 minutes. Add garlic; cook and stir just until fragrant, about 30 seconds. Add carrot; cook and stir 2 minutes more, then stir in frozen peas and green onions.
Add rice to skillet, breaking up any large chunks with your spatula and stir to combine. Drizzle soy sauce and toasted sesame oil over rice mixture and stir. Add pork belly and scrambled eggs; cook and stir until heated through, 1 to 2 minutes more. Taste for seasoning and add freshly ground black pepper and more soy sauce as desired. Serve hot, garnished with green onions if desired.
Notes
You can use any cooked pork belly you like for this recipe, but I highly recommend my Crispy Pork Belly Recipe - it's easy, succulent and has been a reader favorite for years! Note that pork belly varies a lot in leanness / fattiness. The key in step 4 is to make sure you have enough fat in the pan to fry the vegetables and rice, but not so much that you end up with a greasy fried rice. When adding fat at this step, I typically use avocado oil or butter.