Pierogi Dough: Place butter into hot water and stir to melt. Place 4 cups (1 L) of the flour into the bowl of a stand mixer; add hot water and egg. Using dough hook attachment, mix on lowest speed until flour is incorporated, then increase speed to medium and knead for 4 minutes, until smooth and elastic (the dough will be slightly sticky). Wrap dough in plastic wrap and let rest at room temperature while preparing fillings.
Fillings: In a small saucepan, combine peaches, 3 tbsp (45 ml) of the sugar, cornstarch and lemon juice. Cook over medium-low heat, stirring frequently, for about 8 minutes, until peaches are tender and juices are thickened. Scrape mixture into a bowl and let cool for 15 minutes.
Meanwhile, in a food processor, combine eggs, cream cheese and remaining 3 tbsp (45 ml) sugar. Process until smooth. Transfer to a bowl.
Place peach and custard fillings in the freezer, uncovered, for 15 minutes, until well chilled. Transfer to refrigerator to keep cold while rolling and cutting dough.
Cut rested dough into four equal pieces; keeping 3 pieces covered. On a lightly floured work surface, roll out dough to 1/8-inch (2 mm) thickness and cut into twelve to fourteen rounds (discard scraps).
Spoon about 1 tsp (5 ml) of each filling into the centre of each round. Fold one side over filling to make a half-moon shape and squeeze out air while you press and crimp the edges together to seal. Place sealed pierogies on lined baking sheets and refrigerate while you roll and fill remaining pierogies.
Repeat steps with remaining dough pieces and fillings.
To Serve: In a large pot of boiling water, cook pierogies in batches of 6 to 7 at a time, for about 2 minutes or until pierogies float. Using a slotted spoon, remove from water and transfer to a bowl. Repeat with remaining pierogies, bringing water to a boil between each batch.
For each 12 to 14 pierogies, sprinkle with 1 tsp (5 ml) of the sugar, tossing gently to coat. Melt 1 tbsp (15 ml) of the butter over medium-high heat in a large nonstick skillet. Fry pierogies, turning once, for about 2 minutes, until caramelized on both sides. Repeat with remaining pierogies, sugar and butter. Serve hot with fresh peach slices, dollops of whipped cream and mint leaves.
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