Okay, I did not spend my childhood swimming in delicious broth (as far as you know), but when I was little, my father's youngest brother and his wife lived with us for several years. My aunt Claudina and my mom made a number of tasty, tasty Peruvian dishes that I thoroughly enjoy to this day. This soup in particular is pretty good for kids-- it's got a bizarre pinkish-orange hue, noodles and bits of egg to hunt and devour, is often a bit messy to consume, and is not at all spicy. The usual veggie-hiding tactic of finely dicing some zucchini in with the ground beef works pretty well, too.
In a medium-sized pot or a skillet with sufficiently high sides, cook the onion and garlic in the olive oil until almost translucent. Add the tomato paste and ground beef, cook until the beef is browned and the tomato paste has darkened somewhat. Season lightly with salt, pepper, and paprika. Add chicken stock and water*, heat until boiling. Add pasta and cook until almost al dente. Remove from heat and slowly stir in the eggs, allowing them to cook in delightful threads and ribbons. Allow the soup to cool slightly before slowly adding the milk, return to heat and season to taste with salt, pepper, paprika, and oregano. Garnish with fresh oregano, if desired. Serve hot. This recipe serves about 6 people, maybe more or less depending on how hungry you are. It is also almost impossible to eat neatly. Have napkins at the ready and prepare to slurp.
To make this vegetarian, simply swap out the ground beef for either minced veggies (I reccoment sauteed mushrooms and some zucchini) or a soy-based substitute (Gimme Lean ground beef is by far the favorite around here). Veganizing might be trickier, as the eggs provide a distinct flavor and texture that you can't really approximate with anything else. Though if you're okay with eliminating the eggs entirely, just use the milk substitute of your choice along with the veggie 'beef' and broth.
This soup is also delicious the next day in spite of slightly soggy noodles, though it always, ALWAYS seems to need more salt as leftovers. This is a mystery of the universe.
*This is approximately how much I use when making it in a specific skillet of ours-- I don't ever actually measure the ingredients for this soup, so I am not sure. Basically, it is enough liquid that all the meat goodness is hidden, plus a few inches for the pasta to cook in and absorb. If you need to add more water, do so. I do not recommend adding much more chicken broth, though; it will make the soup too salty.