We call it beef noodle, or "neu-zo-mien" in Mandarin. You can find this food everywhere in Taiwan. The pric can be from USD 2.5 to 10 depends on the stores you visit.
I love beef noodles very much, especially the dark one. Because the dark one (the soup looks dark) tastes more stronger and spicy. Some people may like the light version which is not spicy and the soup looks more transparent.
The basic gradients of beef noodles are beef, noodles(of course), vegetables like carrots, onions, tomatoes, grren leaves. For the dark one, it normally contain fermented soy beans with chili, that's what make it the dark look and stronger taste.
I rembered one of my colleague who cam from Germany, he also loves the dark beef noodles very much. He said he can have it everyday and never get tired of it. I guess (just guess) it is because that German people are get used to stronger taste (I mean salty actually).
Hope you will have chances to visit Taiwan, or Taipei maybe, make sure you try this popular food, beef noodle (neu-zo-mien).