Adi Shankaracharya said it was possible to obtain supernatural powers through Vedanta

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Hindus hate that Swami Yogananda and Swami Abhedananda (Vedanta teacher) said that you can obtain supernatural powers like raising the dead through Vedanta (here) because it allows for the discrediting of Hinduism just as the unsubstantiated claims of Eddy's Christian Science to heal the sick proves it is a fraud religion. Hindus will do anything to distance magic powers from Vedanta, including confusing you on whether or not magic powers (called Siddhis) come from Yoga, Siddhanta, or Vedanta, which are all interrelated systems (here, here, and here). However, as you will see below, Vedantist Adi Shankaracharya agreed that Vedanta could lead to Siddhi powers.  The question is not whether Vedanta gives magic powers but whether or not Yoga and Vedanta use the same methods to yield these magic powers. Adi Shankaracharya's exception to Siddhi powers is not their existence but whether or not they should come before or after knowledge of the Vedas, and to acquire them first and then use them to understand Vedas is the wrong way, Vedic study should come first, then magic powers. Christian Science proves itself false by offering magic powers that don't exist, Vedanta does the same thing and can be discredited just as easily. 

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Why does Adi Shankaracharya say magical powers can only be obtained through the Vedas?

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As I discuss in this question, by far the most popular school of Hindu philosophy is the Vedanta school, which bases its tenets on the doctrines laid out in the Brahma Sutras, a work by the sage Vyasa that summarizes and systematizes the philosophical teachings of the Upanishads. You can read the Brahma Sutras here. In any case, the beginning of Adhyaya 2 Pada 1 of the Brahma Sutras, Vyasa says this:

1. If it be argued (that from the acceptance of Brahman as the cause of the universe) arises the defect of the (Samkhya) Smritis being left without any scope, then not so, for otherwise will arise the defect of other Smritis losing their scope.
2. And (Pradhana is not the cause) since the others are not met with (in the Vedas and common experience).

Most commentators agree that in these Sutras, Vyasa is refuting Kapila's Samkhya school. Now in this section of his Brahma Sutra Bhashya, the Advaita philosopher Adi Shankarachrya refutes the objection that the philosophical doctrines found in the Smritis of the Samkhya school should be accepted as valid, since Kapila had extra-sensory perception due to his magical powers:

Nor can we assume that some persons are able to perceive supersensuous matters without Sruti, as there exists no efficient cause for such perception. Nor, again, can it be said that such perception may be assumed in the case of Kapila and others who possessed supernatural powers, and consequently unobstructed power of cognition. For the possession of supernatural powers itself depends on the performance of religious duty, and religious duty is that which is characterised by injunction; hence the sense of injunctions (i.e. of the Veda) which is established first must not be fancifully interpreted in reference to the dicta of men 'established' (i.e. made perfect, and therefore possessing supernatural powers) afterwards only. (The Vedanta Sutras, commentary by Sankaracharya (SBE34), tr. by George Thibaut [1890]  - SECOND ADHYÂYA. FIRST PÂDA. REVERENCE TO THE HIGHEST SELF!)

What Adi Shankaracharya is saying is that magical powers can only be obtained through the injunctions found in the Vedas, so it's invalid to use information gleamed from those magical powers to devise a fanciful interpretation of the Vedas themselves. But my question is, why does Adi Shankaracharya say that magical powers can only be obtained through the injunctions of the Vedas? Are there Yagnas enjoined by the Vedas which yield magical powers?

Now Siddhis or magical powers are mainly discussed by Patanjali's Yoga school; here is what Adhyaya 4 Sutra 1 of Patanjali's Yoga Sutras says about the means of acquiring Siddhis:

janma-oṣadhi-mantra-tapas-samādhi-jāḥ siddhayaḥ

Supernatural powers (siddhis) arise from birth, drugs, mantras, austerity, or yoga (samadhi)

But it's possible that the Vedanta school disagrees with the Yoga school on how to obtain Siddhis. In any case, does anyone know of any references in the Brahmanas or Aranyakas of the Vedas of a Yagna which yields Siddhis?