Brittany Rescigno was about 4 years old when she scrambled her first egg. She grew up in the house next door to her grandparents’ restaurant, the famous Allen’s Clam Bar in New Gretna, and eventually learned every job there was to do there. Her family still runs it, and her dad is also a chef. It’s in her blood.

Now, at age 30, having recently returned to Little Egg Harbor after a stint in California, where her career really took off, she is the new chef at the Delaware Avenue Oyster House in…