Bring 3 quarts (12 cups) water to a boil. Stir in the pastina and salt and cook according to the package directions.
Drain the pasta, reserving the cooking water, and dump the pasta in a bowl or return it to whatever you used to boil it.
While the pasta is still piping hot, add the butter, burying it in the pasta to melt it. Stir in the warm milk. If desired, add a little more warm milk.
Serve at once to prevent the pastina from drying out and clumping. For best results, stir in a little of the reserved cooking water as needed to keep the pasta moist.
Notes
Storage--Store leftover pastina in the fridge in a sealed container for up to 3 days.
Reheating--To reheat pastina, warm it in a saucepan over low heat until heated through. You may need to add a splash of milk to loosen the pasta.