I guess they are called VESA Plug and Display.
That is a Dual-Link DVI-D connector and getting a proper active adapter that will support the full 2560x1600 resolution and actually connect to a Thunderbolt 3 port is not worth the time or money. Some may dispute this, but you will spend $300-$400 for the active adapter and the Thunderbolt 3 dock that has a
single DisplayPort input (OWC Thunderbolt 3 dock).
I would really cut my losses and either buy a 4K DisplayPort or USB-C or TB3 display or simply get a new iMac once an updated one ships.
Someone may have come up with a solution and if you only need 1920X1080p resolution, you might find a cheaper solution, but it will eat up two Thunderbolt 3 port to do it and be a rat's next behind the Mac mini.
Trust me, I tried to get an old 30" Apple Cinema Display up and running on my 2016 MacBook Pro using just a USB-C to USB-A adapter and the Apple Dual Link DVI adapter I had laying around along with a Thunderbolt 3 to Thunderbolt 2 adapter, but the TB3>TB2 adapter does not support DisplayPort signals, so you still have to get a dock in the middle to encapsulate the DP single over Thunderbolt and "sneak" then past the adapter. It's just not worth the time or money.
If someone has come up with a tenable, not horribly janky solution, I encourage you to prove me wrong.