Dimitri Furman shows off a DMV:
As part of our efforts to improve database engine supportability, we have added a new dynamic management view (DMV), sys.dm_os_out_of_memory_events. It is now available in Azure SQL Database and Azure SQL Managed Instance and will become available in a future version of SQL Server. If an out-of-memory (OOM) event occurs in the database engine, this view will provide details to help you troubleshoot the problem, including the OOM cause, memory consumption by the database engine components at the time of event, potential memory leaks (if any), and other relevant information.
Read on to learn more about it, as well as a corresponding Extended Event.