Please find attached herewith three PDFs for your use. I hope you will find a solution to your query regarding a protocol to culture BL21 or Rosetta-gami 2 in minimal media.
Rosetta should grow fine in minimal media. I would suggest doing some controls to make sure everything is as it should be. Try a different strain to be sure the media is correct. Try the Rosetta strain without plasmid to be sure the problem isn't your plasmid being somewhat toxic. It might also just be growing very slowly so be sure you give it enough time (maybe 48 hours)
https://www.genengnews.com/magazine/174/disulfide-bonded-protein-production-in-e-coli/ They use 2% soytone, 1% yeast extract. BUT perhaps you can omit that and still get some inspiration from their protocol - time, temperature, oxygen etc.