Eruv Tavshilin- עירוב תבשילין What? How?

Jewish Law has evolved and developed in some interesting directions, and I'm taking about the strict aka Orthodox, Torah Observant. 

In a year like this one, we Jewish housewives found ourselves in a quandary of sorts. Here in Israel, Shabbat came immediately after the last day of Passover, which is a holiday in itself with the usual HolyDay-"holiday" restrictions. One of those is that cooking is supposed to be for the holiday's enjoyment and not to stock up for later on, even the immediate Shabbat. I guess you can plan on eating leftovers all Shabbat, but that is an insult to the Holy Day.

So Chazal, Our Sages, came up with  Eruv Tavshilin- עירוב תבשילין, which is prepared before the HolyDay, two types of cooked food, specially blessed and put aside for the last Shabbat meal. 

I baked up one of my "bake and serve" one pot vegetable meals, and then I "crowned it" with a slice of matzah.  And before putting it in the fridge, I said the blessing, so all of my Shabbat cooking on the holiday, even something as simple as adding more water to the urn so it would suffice for Shabbat was permitted and kosher.

Of course, none of this will help in a month plus when we have Shavuot coming after Shabbat, since Shabbat is holier, more restrictive than the HolyDay Shavuot. Since then we won't be able to start heating up any of the food on Shabbat for Shavuot, I'm thinking of serving a version of bagels, lox, cream cheese and salad.

When the second day of a holiday falls on Shabbat, as it does this year, or if Shabbat falls immediately after a holiday, it is rabbinically forbidden to cook or bake on the holiday in preparation for Shabbat. Eruv tavshilin is a ritual that, when performed, permits preparation for Shabbat during a holiday. It is interesting to note that there is no prohibition from the Torah to cook or bake during a holiday for Shabbat, and the two reasons given for the allowance are based on the following possibilities:
Either: (a) Shabbat and holidays are considered to be the same day. Since the holidays are referred to as Sabbaths in the Torah, the permission to cook and bake during the holiday is thereby associated with the preparations necessary for Shabbat during the holiday; or (b) in the event of the arrival of unexpected guests, one would need to prepare extra food for the holiday, and Shabbat, by extension, would benefit from these extra preparations.
Why then, if the Torah permits the preparation of food on the holiday for Shabbat, do we need the eruv tavshilin as dictated by the rabbis? Tractate Beitzah offers two explanations for eruv tavshilin. The first is based on the concern of the rabbis of Talmudic times that the needs of Shabbat would be overlooked on occasions when a holiday precedes it, thus they created a unique and tangible preparation for Shabbat that must be attended to before the start of the holiday. The second thought is that rabbis were concerned that by permitting food preparations for Shabbat during a holiday without having a formalized reminder of the exclusivity afforded to Shabbat’s preparations, one might come to make preparations for the subsequent weekdays during the holiday as well. The Torah strictly prohibits preparation for secular days during a holiday or on Shabbat. (OU-Kosher)