Twig Templates : Include dynamic data when using set
The main thing to remember about Twig... You never need to nest tags within other tags. So putting {{ }} within {% %} is never going to work.

To concatenate a string in Twig, use the ~ character...

{% set email = "&lt;a href='mailto:" ~ contactInfo.contactEmail ~ "'&gt;" ~ contactInfo.contactEmail ~ "&lt;/a&gt;" %}