Some Sefardim lay Shimusha Rabba tefillin (mostly at Mincha time), as brought down in the Ariza"l. Is a bracha made over this pair of tefillin?

Shalom, Thank you for your interesting question. The type of tefillin you refer to are quite rare indeed. There are four major ways to order the four parshi'ot (parchments with parts of the Torah written on them) in the head tefillin. The most famous and popular is called "Rashi Tefillin" because Rashi ruled that way. These are the standard tefillin we put on every weekday, and over which we recite the blessing. The next most popular way is that of the opinion of Rabbenu Tam. Many Chassidim and Sephardim put these on in addition to the Rashi Tefillin. Then there are two other ways, which are very rare - one you refer to, the "Shimusha Rabba Tefillin", and then the even rarer "Ra'avad Tefillin". The order of the parshiot in each type is as follows:- Rashi - Ve-haya im shamo’a / Shema / Ve-haya ki yeviakha / Kadesh Rabbenu Tam - Shema / Ve-haya im shamo’a / Ve-haya ki yeviakha / Kadesh Shimusha Rabba - Kadesh / Ve-haya ki yeviakha / Shema / Ve-haya im shamo’a Ra’abad - Kadesh / Ve-haya ki yeviakha / Ve-haya im shamo’a / Shema Even to put on Rabbenu Tam tefillin is recommended only for those who are known for their great piety (See Shulchan Aruch, Orach Haim, 34, 3-4). However, there are communities where Rabbenu Tam tefillin are widespread, especially amongst married men, and someone from such a community does not have to worry about whether they are pious enough to wear such tefillin, and may wear them like the rest of their community. The custom to wear Shimusha Rabba Tefillin at mincha is even rarer - though you are correct that some kabbalists have this practice. For an interesting article on these Tefillin, and all the four types, you should see the talk the last Lebavitcher Rebbe zt"l gave on the fourth day of the shiva for his father-in-law, the Rebbe who immediately preceded him [http://www.sichosinenglish.org/books/proceeding-together-1/02.htm]. There the Rebbe zt"l relates that "In order to put on four pairs of tefillin, one's body has to be exceptionally pure. For with regard to duties obligated by the Torah, such as the tefillin of Rashi and Rabbenu Tam, since "The Torah was not given to the ministering angels," the Torah takes the responsibility upon itself, so to speak. By contrast, with regard to things observed by very few people (the Torah not having obliged everyone to observe them), the individual responsibility is greater. Besides, the very nature of the tefillin of Shimusha Rabba and Ra'avad requires that the body be exceptionally pure." And he adds in a footnote "See Igrot Harames, sec. 5: “The Tefillin of Shimusha Rabba… require an untainted body, and pure and clean thoughts.” R. Menachem Azariah of Fano writes in his Responsa that “these tefillin plumb such deep mysteries that permission was barely granted to use them.” Accordingly, as Ot Chaim (sec. 34) writes at length, most people do not put them on. The author of Emek Hamelech writes in Sha’ar Kiryat Arba. 68: “There is no one who can put on those tefillin, which relate to [the transcendent level of Divinity known as] Arich, and which are arranged according to the teachings of the author of Shimusha Rabba… no man can put them on.” Therefore, I strongly advise you to get a personal ruling from a competent rabbi who knows you well before putting them on at all. In relation to the blessing, the Rebbe zt"l writes (in the same talk) "The tefillin of Shimusha Rabba and, even more so, the tefillin of Ra'avad, relate to a higher level of Divinity than those of Rashi or of Rabbenu Tam. For this reason, none of the authorities hold that one should recite a berachah over them. For the tefillin of Rashi relate to the level of Divinity known as Mochin deImma, and the tefillin of Rabbenu Tam relate to the level known as Mochin deAbba, whereas the tefillin of Shimusha Rabba and of Ra'avad relate to the transcendent level of Divinity known as Keser. Accordingly, [the spiritual energy they generate] cannot be elicited and drawn down by a berachah." But he adds in a footnote there "The author of Atzei Eden (on Menachos, ch. 4) writes that a berachah should be pronounced over the tefillin of Rabbenu Tam when they are being used alone, and the author of Matzas Shimurim holds that the same applies to the tefillin of Shimusha Rabba. See also Torah Or, Shmos 52b." You can also see the Shulchan Aruch ibid, who writes that one does not say a blessing on Rabbenu Tam tefillin. Based on this, one should not say a blessing on these tefillin when wearing them at Mincha, and this is certainly the Sephardic practice. Blessings.