I think you must go with Hotel Management after BBA as it will help you more to become a chef follow your passion. SRM IHM has the unique privilege to be part of one of the premier universities of the world - SRM University. The collaborative approach involves inputs from various departments which gives the benefit of a much wider view and deeper understanding. SRM IHM rewards initiative, novelty and thinking outside the box. Students are individualists of enormous intellectual energy with a talent for collaboration and teamwork. Chain of Hotels recruiters values our graduates for their intellectual abilities, their collaborative mindset, their individuality and their ability to hit the ground running. They invite you to discover the SRM Institute of Hotel Management (SRM IHM) for yourself.( https://www.srmuniversity.ac.in/faculty-of-science-and-humanities/hotel-managment/ )

To become a chef, you can go for a management degree in hotel management that is MBA in HM.

Before that you gain some expertise by getting some work experience in this field and then further join this course. Some of the exams you can apprear for MBA in HM course are CAT, MAT, XAT, ATMA.

This will help you to achieve your goal.

Good Luck.