Heat olive oil in a large skillet over medium heat.
Add diced onion and cook for 3 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground beef to the skillet and cook until browned, breaking it up with a spoon, about 6-8 minutes.
Drain excess grease from the skillet.
Add diced carrots, salt, black pepper, and Italian seasoning to the beef mixture. Stir to combine.
Add water and elbow macaroni to the skillet. Bring to a boil, then reduce heat to low and cover.
Simmer for 10 minutes, stirring occasionally, until pasta is tender and most of the water is absorbed.
Stir in frozen peas and cook for 2 more minutes until peas are heated through.
Remove skillet from heat and sprinkle shredded cheddar cheese over the mixture.
Cover and let sit for 2 minutes until cheese melts.
Serve warm.