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