Make Easiest Ever Pastry Dough: In food processor, combine flour, sugar and salt. Add butter and pulse until mixture resembles coarse crumbs.
Add vinegar and 1 tablespoon ice-cold water, pulsing until dough is crumbly but holds together when squeezed (if necessary, add remaining water, 1 teaspoon at a time). Do not overmix.
Transfer dough to piece of plastic wrap and shape into 1-inch-thick disk. Wrap tightly and refrigerate until firm, at least 1 hour and up to 2 days.
Make Butternut Squash and Feta Tartlets: Heat oven to 400°F. Roll pastry dough between 2 pieces of parchment paper to ⅛ inch thick. Remove top piece of parchment. Using 3-inch cookie cutter, cut out 12 rounds.
Invert a mini muffin pan and lightly grease outside of bottoms and sides. Drape dough rounds over muffin cups to mold into cup shapes.
Bake until cups are golden brown, 18 to 20 minutes. Let cool on wire rack; then carefully remove cups from pan.
In small bowl, combine squash, feta, parsley, and olive oil. To serve, fill cups with squash mixture.