Heat the oven to 400°F (200°C). Cover a baking sheet with parchment paper and set it aside until the assembled pastries are ready.
Place the unsalted butter in a medium saucepan over medium heat and allow it to melt completely.
Stir the packed dark brown sugar, coarsely chopped pecans, and a pinch of salt into the melted butter. Cook for several minutes, stirring from time to time, until the mixture becomes slightly thicker.
Pour in the heavy cream and add the vanilla extract. Continue cooking for 1 additional minute, stirring continuously.
Take the saucepan off the heat and allow the pecan mixture to cool for a few minutes before filling the pastry. Slight cooling prevents the warm mixture from prematurely softening or melting the puff pastry.
While the filling cools, lightly dust the work surface with flour and gently roll out the thawed puff pastry sheet.
Divide the pastry into 6 evenly sized rectangles.
Spoon approximately 1 tablespoon of the cooled pecan mixture into the middle of each pastry rectangle.
Bring the corners of each rectangle inward toward the center, crossing them over one another to create a closed pocket resembling a dumpling.
Beat the large egg in a small bowl until evenly combined.
Brush the beaten egg over the tops of the shaped pastries. This coating encourages an evenly golden finish while also helping the pastry edges remain secured.
Transfer the filled pastries to the parchment-lined baking sheet and place them in the freezer for 10–15 minutes. This short chilling period helps limit spreading and supports a more pronounced puff during baking.
Place the chilled pastries in the preheated 400°F (200°C) oven and bake for approximately 15 minutes, or until the pastry has risen and developed a deep golden color.
Remove the pecan pie bites from the oven and allow them to cool briefly before serving. Serve warm for the best combination of crisp pastry and rich pecan filling.