On a recent Sunday night, Seth Amgott was up until 2 a.m. cracking bones. He and his son had been fishing on the Chesapeake Bay and caught a 25-pound striped bass. While the captain wanted to throw away the carcass, Mr. Amgott, a communications consultant who lives in Washington DC, had a better idea.

“I brought home the carcass in a trash bag,” Mr. Amgott says. That night, his 6-year-old son safely in bed, he sat up making fish stock. His instrument of choice was a stainless steel-lined copper stockpot he bought from cookware...