US Broker-Dealer registered in Belgium needed for IRA

Unfortunately, this sort of thing would have been far easier to sort out if you'd done it before leaving the US. Not sure you're going to find anyone in Belgium that's US registered that you can transfer your IRA to. You would be better advised speaking to a US based financial advisor that deals with expat US citizens. For example here:
https://thunfinancial.com/american-expat-abroad-financial-planning/

It's not a recommendation, as I don't know them, but there is a US registered investment advisor based Belgium. You can see their US registration here:
https://adviserinfo.sec.gov/IAPD/IAPDFirmSummary.aspx?ORG_PK=288211 and if you click on the "part 2, brochure" you can see a description of their services.

Finally, most of the large US mutual fund firms that provide IRA's have U.K. based (and hence EU regulated) subsidiaries. You may want to consider speaking with them.

Try contacting the American Chambers of Commerce Brussels office.
Website: http://www.amcham.be/
Tel. 02 513 67 70
Email: info@amcham.be