Confectioners' sugar and fresh berries, for serving
In a medium skillet, melt 2 tablespoons of the butter. Add the nectarine wedges and cook over moderately high heat, stirring occasionally, until softened, 2 to 3 minutes. Add the brown sugar and cook, swirling the pan, just until dissolved, about 1 minute. Transfer the nectarines to a plate.
In a 9-by-13-inch baking dish, whisk the eggs with the milk and cinnamon. Spread the cream cheese on the bread. Spoon the nectarines on half of the slices and close the sandwiches, pressing lightly. Soak the sandwiches in the egg mixture, turning to coat.
Melt 1/2 tablespoon of the remaining butter on a nonstick griddle or in a large skillet. Add the sandwiches to the skillet and cook over moderately high heat until browned on the bottom, about 5 minutes. Transfer the sandwiches to a plate. Melt the remaining 1/2 tablespoon of the butter on the griddle. Invert the sandwiches onto the griddle and cook over moderate heat until browned on the bottom and cooked through, about 5 minutes. Transfer the sandwiches to plates and sift confectioners' sugar on top. Garnish with berries and serve.