Heat oil and butter in a large skillet over medium-high heat. Add apples and onions, and cook until golden brown, about 15 minutes. Cover, reduce heat to low, and cook until very soft and caramelized, about 35 minutes. Add vinegar and salt, and cook 5 minutes. Let cool.
On a lightly floured surface, roll out dough to a generous 1/8 inch thick. Cut out six 7-inch rounds, gathering scraps and rerolling dough if needed. Place on parchment-lined baking sheets.
Puree half the apple-onion mixture in a food processor until smooth. Using an offset spatula, spread 3 tablespoons apple-onion puree over each dough round, leaving a 1-inch border around edges. Sprinkle each with 2 tablespoons cheese. Season with pepper. Top each with a generous tablespoon of remaining apple-onion mixture, and sprinkle with 2 teaspoons cheese. Fold edges of dough in, crimping with your fingers. Refrigerate until chilled, about 30 minutes. Meanwhile, preheat oven to 350 degrees.
Bake until edges are golden brown, 40 to 45 minutes. Serve tarts warm or at room temperature.