Heat cooking oil in a large skillet or deep pan over medium-high heat.

Add the ground chicken and cook, breaking it up with a spoon, until browned and no longer pink. Drain any excess fat if necessary.

Add the chopped onion to the pan and cook for 3-4 minutes until softened and translucent. If using the optional grated carrot, add it now and cook for 2 minutes.

Stir in the minced garlic and diced bell pepper. Cook for another 3 minutes until the bell pepper starts to soften.

Add the diced tomato (or canned tomatoes), ketchup, salt, and pepper to the pan. Stir well to combine.

Pour in the milk and water (or broth). Bring the mixture to a gentle simmer.

Add the dried pasta to the skillet, making sure it is mostly submerged in the liquid. Stir well.

Reduce heat to medium-low, cover the skillet, and let it simmer for 10-15 minutes, or until the pasta is al dente (cooked but still firm to the bite) and most of the liquid has been absorbed. Stir occasionally to prevent sticking.

If using the optional beaten egg for a richer sauce, quickly stir it into the pasta just before serving, off the heat, until fully incorporated.

Remove from heat and let it sit for a couple of minutes before serving. The sauce will thicken slightly.