Susan Olcott, director of operations at the nonprofit Maine Coast Fishermen’s Association, wants everyone to cook a little more adventurously. “Think of it as ‘seafood beyond lobster,’” she says.

Tricia Reslewic was a young girl when her dad, Mattie, started taking her out on his commercial fishing boat in Massachusetts. Raised in a family of fishermen and great cooks, Reslewic’s life was ...