Generously butter a large 33 x 23-cm (13 x 9-inch) Pyrex dish.
In a saucepan, bring the sugar, brown sugar, corn syrup, molasses, water, vinegar and butter to a boil. Cook over medium heat until a candy thermometer reads 126 °C (260 °F). Remove from the heat, add the baking soda and stir with a wooden spoon just enough to incorporate. Pour into the Pyrex dish and let cool for about 15 minutes. The taffy should still be warm but not hot. Line a baking sheet with waxed paper. Set aside.
When the mixture has cooled enough to be handled, pick up the taffy with buttered hands and begin to stretch and fold the taffy in half and then stretch it again. Repeat this step several times until the taffy fades in color and becomes golden, which take anywhere from 5 to 10 minutes.
Cut the mixture in half. Stretch one piece at a time, into a 1-cm (1/2-inch) in diameter ribbon. With oiled scissors, cut 2.5-cm (1-inch) long candies. Set on the baking sheet until you are ready to wrap them.