Preheat the oven to 350 degrees. Grease and flour (or use nonstick cooking spray) in a mini-muffin pan. Set aside. Roll the dough or pie crust out on a floured surface with a floured rolling pin.
Using a round cookie or biscuit cutter (approximately 3 inches diameter) cut at least 24 rounds out ( or 12 rounds of each pie crust, if using store-bought)
Carefully press each round into the mini-muffin pan. Use your fingers to round the ends into a pie crust. Brush egg wash from one egg to the top edges of each pie.
Sprinkle a small number of chopped pecans into each pie crust. Mix corn syrup, eggs, sugars, butter, and vanilla using a spoon or a rubber spatula. Stir in pecans.
Carefully pour about 2 tablespoons of the syrup into each pie crust. Do not fill past the edge of the pie crusts.
The filling will bubble and rise while baking and you want to avoid it spilling over if possible. This will make them stick when you go to take them out.
Bake for about 22-25 minutes. If the tops begin to brown too quickly after about 15 minutes, you can cover the top with tin foil for the remaining time.
Remove from the oven and allow to cool in the pan for about 10 minutes. Carefully remove from the muffin tin, if you need use a butter knife to slide along the side of the pies to loosen.
Give a little twist and pull them out, and transfer to a wire rack to cool completely. Top with dollops of whipped cream before serving, if desired.