The egg-rich batter to this French-inspired dessert becomes custard-like when baked, while the peaches become soft and bursting with sweetness once exposed to the heat of the oven.
Preheat oven to 375 degrees. In a medium bowl, whisk together eggs and flour until combined. Add sour cream, milk, granulated sugar, vanilla, and salt and whisk to combine. Pour mixture into four 2-cup baking dishes or a 3-quart baking dish. Scatter peaches in a single layer in batter. Bake until custard is browned at edges and center is set, 30 minutes. Let cool slightly. Serve warm, dusted with confectioners' sugar.