Heat the olive oil in a large skillet over medium heat.
Add the chopped onion and diced carrot to the skillet and cook for 3-4 minutes until softened.
Add the minced garlic and cook for an additional 1 minute until fragrant.
Add the ground beef to the skillet and cook, breaking it apart with a spoon, until browned and cooked through, about 6-8 minutes.
Drain any excess fat from the skillet.
Add the elbow macaroni pasta, water, beef broth, tomato sauce, dried oregano, dried basil, salt, and black pepper to the skillet. Stir to combine.
Bring the mixture to a boil, then reduce heat to low and cover the skillet.
Simmer for 12-15 minutes, stirring occasionally, until the pasta is tender and most of the liquid is absorbed.
Stir in the frozen peas and cook for an additional 2 minutes until heated through.
Remove the skillet from heat and sprinkle the shredded cheddar cheese over the top.
Cover the skillet and let it sit for 2 minutes to allow the cheese to melt.
Serve warm.