shabbat - Where is Shabbos called "the most precious of days"?

In our Shabbos tefillos, we say that

חמדת הימים אותו קראת

You (Hashem) called it (the Sabbath) the most precious of days.

In the Shabbos poem "Baruch Keil Elyon" (composed by HaRav Barukh ben Shemu'el, d. 1221) it mentions:

חמדת הימים קראו א-לי צור

The most precious of days my G-d, the Rock, called it

Where did G-d call Shabbos "חמדת הימים"?

Answer

The Beit Yosef to Tur OC 282 quotes the Shibbolei HaLeket (76) that the phrase should be parsed רצית בו וקדשתו חמדת ימים, אותו קראת זכר למעשה בראשית meaning: you wanted it and sanctified it to be the desired of days; it you called as a remembrance to Creation. The Shibbolei HaLeket quotes a Chazzan "Ram" who would emmend the text to to help clarify the meaning. (The Beit Yosef cites an unemmended text, which is confusing. The Derisha there believes the emmendation is adding the phrase זכר למעשה בראשית (see below); the version in the Shibbolei HaLeket has "ואותו" to emphasize the pause before that word; the version in the Machzor Vitri (103) has "וקדשת" to emphasize the connection after that word.)

The Bach there points to Bamidbar Rabbah 10:1 which understands ויכל[ו]‏ as referring to desire (cf. Psalms 84:3) and quotes the Kol Bo as having found a Western Targum that translates ויכל as וחמיד, and while that's still not the version we generally have in our texts, the variant has been attested to. (A number of other Ashkenazi Rishonim mention this variant, though many are unsatisfied with this obscure reference and proceed to give other options.)

Some Nuschaot (eg. the Rambam) have the paragraph end with "קראת" and not conclude with "זכר למעשה בראשית", rendering the suggestion of the Shibbbolei HaLeket problematic. The Avudirham (Shabbat Maariv) explains that קראת here doesn't mean "named" but rather means "designated and sanctified" like in Isaiah 48:12 or Exodus 35:5. Machzor Vitri (103) and Siddur Rashi (477) explain that the phrase means "[Shabbat is] the day that is desired [by the Jews] which you [thus?] called out [to be holy]".

Sefer Ohel Moed (Derekh Eretz) believes that the phrase derives from the Midrash (Bereishit Rabbah 11:8) that Shabbat was a day without a partner and that it and the Jews desired each other as partners.