Unfortunately your talking about something like $100,000 to get custom silicon made, even on an older node size. And you cannot get just 1, your minimum is about 100. If you insist on just 1 then they will still make a 100 and just throw the other 99 away, so you might as well get a 100 of them.
You cannot just throw some Verilog at the fab and get silicon back. You need to use some very expensive software that generates and validates the actual format they need. Hence you would go through a third-party company that specialises in taking your Verilog and does the work needed to get it to the point that the fab can make it.
There are some open source toolchains, such as Yosys [1] and Qflow [2] for synthesising Verilog into ASIC designs that can be fabricated. And with multi-project wafer fab services like CMP and MOSIS, fabrication can be had in the tens of thousands of dollars for a few hundred ICs. So things aren't quite as bad as you make it sound, but it's still a big investment and requires a lot of fairly niche skills and experience.
You cannot just throw some Verilog at the fab and get silicon back. You need to use some very expensive software that generates and validates the actual format they need. Hence you would go through a third-party company that specialises in taking your Verilog and does the work needed to get it to the point that the fab can make it.