There’s no straightforward builtin way to do this from the web UI today.
In recent versions of Phabricator (roughly since https://secure.phabricator.com/D20531 in late May), you can go to “Feed > Transaction Logs”, search for “Object Types: Maniphest Task”, and get a pageable list of human-readable stories about all edits to all tasks. You could use browser search to look through this as a slightly better alternative to browser searching each task, but it’s still very cumbersome. You can export this list to Excel/CSV/JSON and search through it there, which is perhaps slightly better.
Via the API, you can use
transaction.search via the API to retrieve a list of transactions for an object, and since roughly https://secure.phabricator.com/D20209 (late February) this has included details about project changes. This API only operates on one object at a time, but you could write a script to enumerate objects using
maniphest.search, then iterate over them and use
transaction.search to find project changes. This will get you exactly what you want in a repeatable way, but require some upfront investment in writing a script to query the API.
Upcoming changes to Facts (see https://secure.phabricator.com/T13279) may provide a more direct way to access this information via the web UI, but no ETA on that or guarantees it will actually be available.