Set a large Dutch oven or a deep skillet over medium-high heat and add the 1 tablespoon of olive oil. Drop in the ground beef, diced yellow onion, and green bell pepper, cooking for 5 to 6 minutes while continuously breaking the meat into small, uniform crumbles until it is entirely browned and the vegetables have softened.

Tilt the pan slightly to ladle out or drain away any heavy excess pooling grease, leaving just a thin coat of flavorful lipids to gloss the ingredients, then reduce the stove heat to medium.

Add the minced garlic and the 1 tablespoon of tomato paste straight into the center of the pan, mashing and stirring them against the hot metal surface for exactly 1 minute until the paste blooms into a deep rust color and fragrant aroma.

Pour the tomato sauce, diced tomatoes with their juices, beef stock, Worcestershire sauce, dried Italian seasoning, kosher salt, and black pepper directly into the meat matrix, stirring firmly to scrape up any browned bits stuck to the bottom of the pot.

Drop the 1 cup of uncooked elbow macaroni straight into the liquid sauce, tossing completely so the raw noodles are fully submerged. Bring the pot up to a rolling boil over medium-high heat, then immediately drop the flame down to low to maintain a gentle simmer.

Cook uncovered for 10 to 12 minutes, stirring the mixture every few minutes to keep the loose pasta starches from anchoring or burning on the bottom of the pan. Once the noodles have absorbed the liquid, plumping up into tender, sauce-flooded tubes, stir in the 1 cup of shredded sharp cheddar cheese until it completely melts and strings throughout the beefy gravy, then pull from the heat and serve immediately.