No noodles are actually called "brown noodles" but the only noodles I'm aware of that are brownish in colour are either wheat or buckwheat.
Given the suggestion to cook it with a "protein source", and given that this is meant to be a quick and easy meal, I'm sure that the idea was to cook some dried noodles briefly in soup along with some sliced or shredded meat. This is common in Asian cuisine, and it can be nutritious, assuming you don't rely on instant noodles and artificial flavour packets.
You'd probably be looking at one of the following:
Ramen, which is traditionally made from la mian (hand-pulled buckwheat noodles, although sometimes they're made from wheat), served in broth, usually with meat and green onions, and often flavoured with soy sauce. Keep in mind that real ramen is actually quite difficult and time-consuming to make, and is not even close to the "instant ramen" you see for 99 cents a package. You can cheat a little and still have a decent meal by buying quality dried noodles and cooking them in real homemade broth, or at least canned broth.
Udon, AKA "thick noodles" (made from wheat), which are also typically prepared in broth, specifically dashi - broth made from kombu (kelp), dried tuna or bonito flakes, and occasionally mushrooms, and seasoned with soy sauce and mirin (rice wine). Meat isn't as common in udon, but fish and tofu are, especially deep-fried. You can still make it with beef or chicken. You can find decent-quality instant dashi at Asian grocery stores, so again, prep time is minimal if you get the right ingredients.
Soba (buckwheat) noodle soup, which (in my experience) is almost always served in miso (again, available in instant form). Seasonings and toppings are otherwise similar to udon, although they tend to get a bit more elaborate. For example, the wiki page references tsukimi soba which means poaching a raw egg in the cooked soup.
Finally Phở, which is the Vietnamese take on this, which uses rice noodles (so definitely not brown). The most common preparation (at least in all of the Vietnamese restaurants around here) is simply the hot soup and noodles with some rare beef dropped in to briefly cook, then topped with basil and bean sprouts just before eating. The broth is really very difficult for non-natives to learn and instant pho is usually terrible, so I wouldn't recommend this for beginners.
Of course you can always just go with good old-fashioned Western chicken noodle soup or chicken soup with rice and vegetables. Chicken noodle soup usually uses egg noodles, which are, again, definitely not brown, so although they're a fine choice, they're almost certainly not what the question is referring to.