Line 12 muffin cups with square sheets of waxed paper.
Heat white sugar, brown sugar, evaporated milk, and frozen orange juice concentrate together in a heavy-bottomed saucepan over low heat; cook and stir until sugar dissolves, 2 to 3 minutes. Stir vanilla extract into the sugar mixture. Fold pecan pieces through the mixture. Cook without stirring until the mixture reaches a temperature of 235 degrees F (113 degrees C), 5 to 10 minutes; remove from heat immediately.
Stir candy mixture until it begins to turn opaque and stiff but can still be spooned easily; spoon into prepared muffin cups.