I'm having the same issue. Not sure which version of Typescript you're on, but I'm on 3.4.1. It appears to be a known issue – see Issue #30663 on GitHub.
I've temporarily downgraded to 3.1.1 and it seems to now be compiling at a reasonable speed.
The newest version said that it had a speed enhancement. That might help. Also, that issue (30663) has been fixed.
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