This was originally reported in micrometer-metrics/micrometer#1011.
HttpRequestMethodNotSupportedException prevents timing in WebMvcMetricsFilter and a simple fix seems to be just ignoring HttpRequestMethodNotSupportedException in filterAndRecordMetrics() and using null handler but I'm opening an issue in case there's a better approach for it. If ignoring HttpRequestMethodNotSupportedException is a right approach, I can create a PR for it.
Here is a sample project to reproduce it: https://github.com/izeye/sample-micrometer-spring-boot/tree/micrometer-gh-1011-2.1.0
Reproduction steps as follows: