If you’re headed to New Orleans and you mention it to anyone, you’ll be directed to the boundless joys of muffulettas and po’ boys, gumbos and étouffées, red beans and rice and jambalaya.

This list goes on, an American canon built by overlapping culinary influences in what was once a hub for Indigenous tribes and later the trans-Atlantic slave trade, shaped and reshaped by hundreds of years of colonial rule and immigrant flux.

Every city has its greatest hits from another century, its repertoire of untouchable classics, but New Orleans is so loaded with them, it can seem a little unfair. It can also give a visitor the wrong impression — as if, somewhere back there, the city got stuck in time.

No, the juice is always running here, and those influences keep bopping together deliciously. Call the Gulf whatever you want. At Acamaya, the chef Ana Castro insists on the connection between Louisiana and Mexico.

Ms. Castro nixtamalizes heirloom corn to make chochoyotes, and lately she has immersed the pudgy, dimpled masa dumplings in a slippery green sauce, lush with sweet crab meat, prickling with the warmth of poblano chiles and peppery nasturtium leaves.