Heat the olive oil in a large pot over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks.
Stir in the diced onion, minced garlic, and sliced carrots. Cook for 5 minutes until the onion softens.
Pour in the beef broth and diced tomatoes. Season with salt and pepper, then bring the mixture to a simmer.
Add the egg noodles directly to the pot. Cook for 8 to 10 minutes, stirring occasionally, until the noodles are tender.
Remove the pot from the heat and stir in the grated Parmesan cheese until it melts into the broth.
Sprinkle with chopped parsley before serving.