In this article an Orthodox woman describes how her rav permitted her to enroll in culinary school. Although he apparently did not permit cooking meat and milk together, is there any angle to permit this professionally in a non-kosher restaurant?
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Per this article at ohr.edu there are 2 possibilities where one may cook meat with milk.
A Jew may not cook Basar BeḤalav of a Behemah Tehorah, even a Nevelah. This means that a cow, goat, sheep, or the like, may not be cooked with milk, even if the animal died of natural causes or was slaughtered in a method that was not in accordance with Halachah. On the other hand, cooking a Ḥayah Tehorah, such as venison, is permissible and is not banned even MiDeRabanan. The same is true for a Behemah Temeiah.
HOWEVER, the RaM"A holds that there is even a Marith 'Ayin issue of cooking a Ḥayah Tehorah or Temeiah or Behemah Temeiah with milk of a Tehorah, and it is therefore forbidden. The Sha"Ch disagrees (the Ta"Z wants to disagree but defers to the RaM"A).
Source: Y"D 87:3 (and see this answer for more information).