By the 1930s, when Tyler boasted more than one shochet, Samuel Greenberg was selling smoked kosher turkeys to Jews and non-Jews alike.

He rubbed those birds with a spice mix attributed to his mother, Jennie Greenberg. Working in a metal shebang with a sand-covered floor, tucked in a back corner of his milking barn, Greenberg and Elva Cole, a black colleague who probably stoked the pits, hung the turkeys from a nested pair of ceiling-mounted wagon wheels and smoked them over hickory logs.

Few records of the early days of the business remain. But every Greenberg tells the story of the six turkeys ordered in 1938 by a Dallas customer. Purchases were traditionally picked up on the farm, so they had to figure out how to get the turkeys to Dallas, about 100 miles west. Zelick Greenberg, a son of Samuel, packed the turkeys in a candy store box, added straw for cushioning, and shipped them by rail from Tyler.

Word of Samuel and Zelick Greenberg’s work spread by mouth. And by rail. And soon by mail. The birds that arrived on the other end were not typical smoked turkeys. “What my father did was not a casual smoke,” said Sam Greenberg, a ruddy-faced 52-year-old, who may never have met a stranger.

“Those turkeys weren’t honey-colored, they were really, truly smoked,” Mr. Greenberg said, his voice rising to a shout, as if an increase in volume could convey the intensity of the charred hickory fog that permeates his family’s turkeys, rendering the birds a color best described as burnt umber with a black licorice wash.