Review גמרא דף לט. “ולא יפקיענה בסודרין (five lines from top of the Amud) until “ולא יטמיננה בחול (next set of two dots)
See רש”י דף לט. “דשרי who says the reason it is permitted to cook something directly from the sun is because “אין דרך בישול בכך”
Major Question:
We have a rule in הלכות שבת when a melacha is performed in an abnormal way it is exempt from Torah violation however it is still prohibited מדרבנן. So how could it be permitted to cook directly from the heat of the sun?
There are prohibitions of cooking in regards to other halachos. For example – cooking meat and milk together, cooking the Korban Pesach.
If someone were to cook in the sun or a product that was heated by the sun would they be transgressing that prohibition?
See גמרא פסחים דף מא. “אמר רב חסדא המבשל (ten lines from bottom of the Amud) in regards to cooking the קרבן פסח in חמי טבריא.
https://hebrewbooks.org/shas.aspx?mesechta=4&daf=41&format=pdf
See רמב”ם ה’ מאכלות אסורות פרק ט הלכה ו in regards to cooking meat and milk together in חמי טבריא
https://hebrewbooks.org/pdfpager.aspx?req=58960&st=&pgnum=133
Learn אגלי טל מלאכת אופה ס”ק מד
https://hebrewbooks.org/pdfpager.aspx?req=14401&st=&pgnum=264
https://hebrewbooks.org/pdfpager.aspx?req=14401&st=&pgnum=265
Learn אגרות משה או”ח חלק ג ס’ נב who gives a different explanation than the אגלי טל
https://hebrewbooks.org/pdfpager.aspx?req=919&st=&pgnum=351
https://hebrewbooks.org/pdfpager.aspx?req=919&st=&pgnum=352
Based on the above would cooking in a microwave be a violation from the Torah, Drabanan, or permitted barring the operation of electric appliance on Shabbos
See שו”ת מנחת שלמה קמא ס’ יב הערה ו & ז for a new explanation different than the אגלי טל and אגרות משה
https://hebrewbooks.org/pdfpager.aspx?req=15096&st=&pgnum=149
https://hebrewbooks.org/pdfpager.aspx?req=15096&st=&pgnum=150