Heat olive oil in a skillet with a tight-fitting cover over medium-high heat.
Add diced onion, green bell pepper, minced garlic, ground beef, dry mustard, chili powder, kosher salt, and black pepper. Sauté until the ground beef is no longer pink, breaking it up as it cooks. If needed, drain any excess grease.
Stir in the uncooked white rice and cook for two minutes, allowing the rice to absorb the flavors.
Add tomato paste and cook for an additional minute.
Pour in the diced tomatoes with juice, water, and Worcestershire sauce. Stir everything together, cover the skillet, and simmer for 20 minutes.
After 20 minutes, remove the lid and fluff the mixture with a fork. If the mixture appears too wet, cook for a few extra minutes with the lid off.
If desired, sprinkle shredded cheddar cheese on top during the last few minutes of cooking time with the lid on.
Serve this delicious Texas Hash hot and enjoy its hearty flavors!