In a medium saucepan set over medium heat, melt the olive oil and butter together.
Add the rice and stir to coat with the oil and butter. Cook, stirring frequently, for about 2 to 3 minutes until the rice is lightly toasted.
Stir in the chicken broth, tomato sauce, chili powder, cumin, garlic salt, oregano, and diced tomatoes, if using, until well combined.
Increase the heat to high and bring the mixture to a boil, stirring occasionally to ensure even cooking.
Once boiling, stir well, reduce the heat to low, cover the pot with a lid, and let it simmer gently for about 20 minutes or until the rice is tender and the liquid is absorbed.
If the rice is not tender or there is still unabsorbed liquid after 20 minutes, replace the lid and cook for an additional 2 to 4 minutes as needed.
Remove the pot from heat, keep it covered, and let the rice rest for a few minutes. Fluff the rice with a fork before serving to separate the grains.