Preheat the oven to 350°F (175°C).
Heat olive oil in a large ovenproof skillet or casserole dish over medium heat.
Add the diced onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Add the ground beef to the skillet, breaking it up with a spoon, and cook until browned and no longer pink, about 6-8 minutes.
Add the diced carrots, red bell pepper, and sliced mushrooms to the skillet. Cook for 5 minutes, stirring occasionally.
Stir in the diced tomatoes with their juice, beef broth, tomato paste, dried oregano, dried basil, salt, black pepper, and smoked paprika.
Bring the mixture to a simmer and cook for 10 minutes to allow flavors to meld.
Stir in the frozen green peas.
In a small bowl, mix the cornstarch with cold water until smooth. Stir this slurry into the casserole to thicken the sauce.
Cook for an additional 2-3 minutes until the sauce thickens.
If using, sprinkle shredded cheddar cheese evenly over the top of the casserole.
Transfer the skillet or casserole dish to the preheated oven and bake uncovered for 20 minutes, until the cheese is melted and bubbly (if using).
Remove from the oven and let the casserole rest for 5 minutes before serving.