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In United States, the ones I have heard something nice about, that offer a professional program in Buddhist Studies:
Many large universities in US offer a program in philosophy (or "comparative philosophy") with concentration in buddhist studies. See for example this list from the Tricycle magazine. Buddhist studies further specialize into Early&Theravada Buddhism, Indian-Tibetan Buddhism, and Chinese/Korean/Japanese Buddhism.
In my understanding, the way this (the choice of school for PhD) is usually done is: you find yourself drawn to one of those subfields of buddhist studies and realize that you keep enjoying online articles and published books by a particular professor from a particular college. Then you go to that college and study under that specific professor or one of his/her students. Like, you're definitely supposed to know much of the professor's work before you even show up as potential PhD candidate.
Also note that since studying Buddhism academically involves studying texts, the student at PhD level is expected to know a couple of primary languages (Pali, Sanskrit, Tibetan, Chinese) and a secondary language (usually French, since most early 20th century study of Buddhism was in that language, or perhaps Japanese or Korean if that's what you study).
Which is why you can't simply jump from a Master's in Engineering to a PhD in Buddhism. You need to start at the grad level and get the basic background in languages, history, culture, and philosophies of the geographical area corresponding to your preferred type of Buddhism.
A slightly less academical and more pragmatic approach is to pursue a degree in "Buddhist Ethics". I believe this usually helps avoid getting pigeonholed into a specific geohistorical tradition, and gets a more "applied" perspective on Buddhism, relevant to the real life in the modern society. Buddhist Ethics is something you'd get if you want to practice Buddhist leadership as opposed to doing research and translation.
Finally, if you dream of becoming a professional Buddhist Chaplain (a "priest"), you may want to consider pursuing the Master of Divinity degree. There is one now offered by the Harvard Divinity School and a number of less famous schools such as University of The West in LA and Maitripa College in Portland.
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In the west it's most of the time part of a more broad study, I believe. In the country where I live you can become Buddhist Spiritual Guidance Counselor. And then there are studies like this one, fi.: https://religiousstudies.mcmaster.ca/graduate/graduate-program
Sri Lanka has an university: http://www.bpu.ac.lk
Another idea might be studying the autobiographies of monks. Especially of scholar monks. Most of the time it is mentioned where said monk has gotten his degree. This could give you some opportunities.
Hope this helps.
Upvote:2
You can consider the Doctoral Program in Buddhist Studies of the Ludwig-Maximilians-UniversitΓ€t MΓΌnchen (University of Munich) in Germany.
According to the DAAD page for this course, there are no tuition fees. You can get funding from The Robert H. N. Ho Family Foundation Program in Buddhist Studies (please see this answer). You can also get some funding from the University of Munich's "Global Cultures β Connecting Worlds" program.
The guidelines for this program state:
The prerequisites for admission to the doctoral program are proof of completion of a Master of Arts or Magister Artium degree in a relevant field, knowledge of at least one Buddhist source language and outstanding qualification in the subject.
A Buddhist source language is presumably one of these: Pali, Sanskrit, Tibetan, Chinese.
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There's an Oxford Centre for Buddhist Studies in the UK.
There are other Centres for Buddhist Studies in Toronto, Hong Kong, Bristol, London, Denmark, India, Kathmandu; also Hamburg; similarly an Institut d'Etudes Bouddhiques in France; and so on.