To the empty area in the middle of the pan, add olive oil. Using a spatula, spread the olive oil around the empty area. To the middle of the pan, add the fideo pasta. Drizzle olive oil on top of the pasta.
Using a spatula or large spoon, continuously stir the pasta. Keep stirring the pasta as starts to brown. Keep a close eye on the pasta so that it doesn't burn. If the pan gets too hot, remove it from the burner and keep stirring the pasta.
Once the fideo noodles start to brown, add the chopped garlic to the pan. Stir. To the pan, add the canned tomatoes and broth (or water). Stir. If the pan isn't large enough to add all of the broth, add as much as possible and then as the broth reduces, add the remaining amount to the pan.
When the liquid starts to reduce, add the butter, cumin, oregano, salt and pepper. Stir together. To the pan, add the cooked pieces of chicken and stir together. Do a quick taste test and add more salt if needed.
Serve warm. There should be some liquid left in the pasta mixture when serving. If there's not enough broth left in the skillet, just stir in more chicken broth or water.