In a large bowl, whisk together the egg, milk, water, and sour cream. Stir in the flour a little at a time, until the mixture comes together and forms a dough. Turn dough out onto a lightly floured surface, and knead until smooth and elastic, about 10 minutes. If the dough is sticky, it may be necessary to incorporate a little more flour. Cover the dough with plastic wrap, or an inverted bowl, and let rest for 1 hour.
In a small bowl, combine creme fraiche, 2 tablespoons sugar, and vanilla; set aside.
Line a baking sheet with a clean tea towel and sprinkle generously with cornmeal to prevent sticking. On a lightly floured surface, roll out the dough 1/8-inch-thick. Cut out circles using a 3 to 4-inch round cutter. Place 1 half apricot or peach onto each circle. Sprinkle the cavity with a little sugar and place another 1/2 on top. Lightly moisten edges of dough with water. Fold dough over to enclose fruit and seal by pinching. Transfer to prepared baking sheet.
Preheat oven to 200 degrees F.
Bring a large pot of salted water to a boil. Add pierogies, in batches, and boil about 5 minutes (until they float to the surface), while stirring occasionally with the handle of a wooden spoon to prevent sticking. Meanwhile, melt butter in a skillet and pour onto a large ovenproof platter to cover. Drain pierogies and transfer to platter. Sprinkle with sugar and place in oven to keep warm while cooking remaining pierogies. Serve warm with dollop of sweetened creme fraiche.
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