Heat the olive oil in a large skillet or Dutch oven over medium heat.
Add the Italian sausage and cook for about 5 minutes, breaking it apart as it cooks, until browned and cooked through.
Add the diced green bell peppers and onion to the skillet.
Cook for about 5 minutes, stirring occasionally, until the vegetables begin to soften.
Stir in the garlic, salt, pepper, oregano, and basil.
Cook for about 2 minutes, allowing the garlic and seasonings to become fragrant and blend into the sausage mixture.
Pour in the chicken broth and use a spatula to scrape up any browned bits from the bottom of the skillet. Those bits add incredible flavor to the dish.
Stir in the tomato sauce and jasmine rice.
Cover the skillet and reduce the heat to medium-low
Simmer for 15–20 minutes, or until the rice is tender and has absorbed most of the liquid.
Remove the lid and fluff the rice with a spatula or fork.
Sprinkle the mozzarella cheese evenly over the top, followed by the Parmesan cheese.
Allow the cheese to melt before serving.