1. In a large skillet or pan, cook the ground beef over medium-high heat until browned. Break it up into crumbles as it cooks. Drain any excess fat.
2. Add the chopped red onion and minced garlic to the skillet with the beef. Saute for a few minutes until the onion becomes translucent.
3. Stir in the diced tomatoes, including the juice from the can. Season with salt and pepper to taste. Let it simmer for about 5 minutes.
4. Add the pasta to the skillet along with the milk. Bring the mixture to a gentle boil, then reduce the heat to low. Cover and simmer for about 15-20 minutes, stirring occasionally, until the pasta is cooked and the sauce has thickened.
5. In a small bowl, beat the eggs. Slowly pour the beaten eggs into the skillet, stirring continuously to incorporate them into the sauce. This will thicken and enrich the sauce.
6. Add the butter to the skillet and stir until it melts and combines with the sauce.
7. Taste and adjust the seasoning as needed with more salt and pepper.
8. Once the pasta is cooked to your preferred tenderness and the sauce has thickened, remove the skillet from the heat.
9. Let the skillet rest for a few minutes before serving to allow the flavors to meld together.
10. Serve the tomato beef pasta skillet hot, garnished with some fresh herbs or grated cheese if desired.