The question arises whether it is permissible to add hot water to instant soup mixes on Shabbat. While, of course, it is prohibited to cook on Shabbat, can the principle of "En Bishul Ahar Bishul" (there is no prohibition to cook a food which has already been cooked) be applied, since the ingredients of the soup mix may already be cooked and then freeze-dried?
Hacham David (Halacha Berura, Hilchot Shabbat p. 485-Refer to Audio for Hebrew Quote) writes that that even if many ingredients were cooked, there may be some minor ingredients, such as spices, which remain raw. Pouring hot water on them would constitute Bishul. The process differs between different manufacturers. Therefore, one may not be lenient unless he verifies with certainty that ALL the ingredients were previously FULLY cooked.
Moreover, even if all the ingredients were fully cooked, it is possible to argue that the principle of "En Bishul Ahar Bishul" would not apply, since, in this case, the cooked ingredients need the hot water to become edible as soup. Thus, the second "cooking" has an impact and may be prohibited.
It may even be prohibited to use hot water from a Keli Sheni, as these ingredients could constitute "Kaleh Bishul"-easily cooked items, similar to tea leaves, in which the water from the Keli Sheni is just as effective as water from a Keli Rishon.
Nevertheless, Hacham David does permit pouring hot water from a Keli Shlishi on to any soup mix, as the Halacha established that Keli Shlishi never cooks. This means, one may pour hot water from the urn (Keli Rishon) into a cup (Keli Sheni) and then from that cup into a different cup (Keli Shlishi) and pour the mix into that cup. It is also permitted to pour directly from the Keli Sheni onto the soup mix; this is equivalent to Keli Shlishi.
SUMMARY
One may not prepare instant soup mixes with hot water in a Keli Rishon or Keli Sheni on Shabbat, but he may do so with a Keli Shlishi.