Per the folks at WPEngine:
I've disabled the "popover" plugin. It's running this query, which alone takes 20+ seconds to complete.
SHOW TABLES LIKE 'wp_7331_popover';
Your development team either needs to enable object caching so that the value doesn't have to be calculated over and over again, or reach out to the developer of the plugin to correct this issue. Here is a helpful guide on object caching: