VMware officially supports the Apple Mac Mini, see the VMware Compatibility Guide. However, since the Apple Mac Mini is not an Enterprise-class system but instead a consumer system without Error-Correcting Code (ECC) memory, issues including software crashes can occur. This document outlines some of the common issues that may occur when running ESXi on such consumer grade devices and outlines some basic steps that you can troubleshoot before contacting VMware Support.
During the system crash, if a machine check exception (MCE) is thrown and a purple diagnostic screen displays, a hardware problem has caused it. There is no other way to generate an MCE. You should work with their hardware vendor to replace the faulty system. If an MCE is not thrown and a purple diagnostic screen displays, it may still be related to a hardware issue and before contacting Broadcom Support, ensure you can consistently reproduce the issue on another system using the exact workflow which caused the initial system crash.
Here are some basic troubleshooting steps that you should run through prior to contacting Broadcom Support:
Note: vSphere running on Apple hardware platform is an officially supported configuration from Broadcom. But it is not a published configuration from Apple Inc. If any support call results in perceived hardware issue, you are expected to resolve the issue directly with Apple and/or your hardware vendor.