To begin the pastry, combine the flour, sugar, and salt in a large mixing bowl. Add the cold, cubed butter and blend using a pastry cutter or your fingers until the mixture resembles coarse crumbs with pea-sized pieces of butter. If using a food processor, pulse the dry ingredients, then add butter and process to a crumbly consistency.

Gradually stir in 2 to 3 tablespoons of cold water, kneading lightly until the dough coheres into a smooth ball. Additional ice water may be added as needed. In a food processor, pulse with water until dough begins forming a ball, then bring together by hand. Form the dough into a thick disc, wrap in plastic wrap, and refrigerate for at least one hour or up to a week.

Roll out the chilled dough on wax paper to a moderate thickness, avoiding excessive thinness. Use a round cutter or bowl (3.5–4 inches in diameter) to cut circles. Fit each into the cups of a 12-cup muffin tin, pressing the dough gently to shape along the base and sides. Any tears can be mended by pressing the dough with a fingertip. Freeze the prepared shells for 10–15 minutes.

Meanwhile, preheat the oven to 350°F (177°C). In a large bowl, whisk together brown sugar, corn syrup, melted butter, eggs, vinegar (if using), and vanilla extract until well combined.

Distribute the filling evenly among the tart shells using a ladle, filling just below the rim. Bake in the preheated oven for 20 to 25 minutes, or until the crust is golden and the filling appears set and slightly puffed.

Allow the tarts to cool in the pan for 10 minutes before transferring to a wire rack to finish cooling.