How would you transcribe and/or describe this vowel?

The speaker in your video link is not a speaker of Southern American English, which is the accent most likely to split phonemic /æ/ into phonetic [æjə], which can be perceived by folks with other regional accents as realized in two syllables separated by a glide providing a sort of hiatus between the two halves, although the line between a disyllabic [æjə] and monosyllabic [æə̯] is not always clear to my casual ear.

Possibile phonetic realizations of phonemic /æ/ mentioned in the Wikipedia article on /æ/ or short-a raising and tensing include all of:

1. [æ]
2. [æː]
3. [æ̝ˑ] <-- look at this one
4. [æɛə]
5. [æjə]
6. [eː]
7. [eə]
8. [eɪ]
9. [ej]
10. [ɛː]
11. [ɛə]
12. [ɛj]
13. [ɛjə]
14. [ɛɔ]
15. [ɪə]

Of those, number 3’s [æ̝ˑ] version has a particular diacritic ̝ written beneath the æ, which indicates a slightly raised version of that vowel. It also uses the ˑ modifier after it to mean that it’s a little longer than normal but not quite so long as a full ː modifier would mean.

So that might well be the first part of the sound you’re hearing at the point in the video that you’ve drawn attention to. Because she is saying the sound carefully in isolation, she may be accentuating those two effects.