There is a knack to filling in the PIP forms and using the correct wording on each of the descriptors to say how Asperger's effects you.
Firstly you need to gather evidence from your GP for a claim and make an appointment to say you are going to apply for PIP and tell your GP how it effects you on a daily basis so your notes have that evidence.
One thing, as a mother of a son with autism, I fill in People's PIP forms regularly and they tend to underestimate the impact their condition has on them and not put too much detail in. Make it as detailed as possible. See a Welfare Advice worker for their help if possible at a Citizens Advice Centre if you still have one...many have been cut by local councils due to lack of funding.
Have you definitely got a specific diagnosis of having Autistic Spectrum Disorder? That is the starting point. Many do not and the DWP advisor won't look at it without a firm evidenced diagnosis. Many people with Asperger's Syndrome put just that on the form. Instead use the term "I have Autistic Spectrum Disorder" . I have noticed over time just how many people with Asperger's get turned down when they put Asperger's Syndrome on the form...DWP advisors automatically think you are very high functioning to the point you need no help. You are on the autisitic spectrum so say so!
The cooking descriptor is not enough to be awarded the standard component of daily living allowance. You need to look through the forms and see how each of the descriptors effect you personally.
An excellent resource with examples for filling in the PIP form is Benefits and Work
https://www.benefitsandwork.co.ukYou can get free access but if you pay the £19.95 yearly payment you will not regret it and have access to a whole lot of PIP resources that could help you. Preparation and research is the key to filling in a PIP form. I allow myself a week to slowly fill it in bit by bit for whomever I am helping and will use extra sheets and go into great detail.
Please please please ensure you firstly reply on time, Once they send you the forms you get a very tight 3 week window to reply and when sending your forms back, send them by signed for recorded delivery as so many get lost and you then have no proof they have arrived at the DWP.
They will then either call you to an assessment centre for a face to face appointment to assess your disability themselves or in certain areas they will come to your home...it depends entirely on the area. You can have someone with you who for support. You can record the assessment if you tell them when making that appointment and they have to facilitate this.
Good luck with it all. It is a very tricky system to navigate alone, so please get expert help and advice before you send for the forms and during the process.