Put oven rack in middle position and preheat oven to 375°F. Cook onion, butter, water, salt, and pepper, covered, in a 10-inch heavy skillet over moderately low heat, 10 minutes. Remove lid and cook, stirring frequently, until onion is deep golden brown and very tender, about 25 minutes. While onion cooks, roll out dough to slightly less than 1/8 inch thick. Cut out 12 rounds with cutter and lightly press each into a mini-muffin cup. Bake until pale golden, 10 to 12 minutes. Remove tartlet shells from muffin pan. Stir together creme fraiche and chives and divide among shells, then top with caramelized onions.