Heat the olive oil in a large skillet over medium-high heat.
Add the ground beef and cook, breaking it apart with a spoon, until browned and cooked through, about 5-7 minutes.
Add the diced onion, minced garlic, diced red bell pepper, and sliced carrot to the skillet. Cook, stirring occasionally, until the vegetables begin to soften, about 4 minutes.
Pour in the beef broth and the can of diced tomatoes with their juice. Stir to combine.
Add the egg noodles, dried Italian seasoning, salt, and black pepper. Stir well to submerge the noodles in the liquid.
Bring the mixture to a boil, then reduce heat to medium-low. Cover the skillet and simmer until the noodles are tender and most of the liquid is absorbed, about 10-12 minutes. Stir occasionally to prevent sticking.
Remove the skillet from heat and sprinkle the shredded cheddar cheese evenly over the top. Cover again and let sit for 2-3 minutes until the cheese melts.
Garnish with chopped fresh parsley before serving.