Generously butter a 10×15-inch (25×38 cm) baking pan; set aside.

In a medium saucepan over medium heat, combine the brown sugar, white sugar, and butter. Stir until the butter melts and the mixture starts to bubble.

Attach a candy thermometer to the pan. Cook, stirring occasionally, until the mixture reaches the soft-ball stage (238 °F / 114 °C).

Remove the pan from heat. Quickly stir in the vinegar and vanilla extract, then place the pan on a damp kitchen towel to stabilize.

Beat the mixture vigorously with a wooden spoon until it thickens and loses its glossy sheen, about 3–5 minutes.

Working quickly, drop teaspoonfuls of the hot candy onto the prepared baking pan. Leave space between each drop.

Allow the butterscotch candies to cool and set at room temperature for at least 20 minutes before removing them.