Nicki Minaj at Steakhouse -- Bring Me Some A.1. Sauce, STAT!!!

Nicki Minaj committed the ULTIMATE steakhouse sin at Boa last night ... she sent someone out to get her A.1. Steak Sauce right in the middle of her meal ... and TMZ has the video proof!!!

FYI -- most chefs working at top steak joints across the globe consider a request for A.1. sauce (or any other sauce not made by the restaurant) as a total insult ... an insult proudly committed by millions of people every day. It's right up there with asking for your steak cooked "extra well-done and butterflied."

But last night in Hollywood, Nicki -- who was eating with her BF Safaree -- proved she doesn't give a damn ... 'cause after she sat down, TMZ cameras captured someone running in a bottle of A.1., specifically for Nicki's table.