Node environment variables not recursively expanded

A user reported a problem whereby a script

node('some-slave') {
  sh 'echo hello'
}

would fail, claiming the shell interpreter could not be found. In fact

echo env.PATH

revealed a mangled path like

/usr/local/bin:$PATH:$SOME_TOOL/bin

with various unexpanded variables. The node in question had the custom environment variable property set, where in particular PATH was set to an expression involving $PATH as well as various other sister properties.

Freestyle projects were building without problem on this node, so it seems that the Workflow node step was failing to expand variable references picked up from the custom property.