To make Pie Pop Filling:
Preheat the oven to 325 degrees F.
Whisk the eggs in the bowl of an electric mixer. While the eggs are mixing take a small saucepan
and set it over medium-high heat. Add the butter
to the saucepan and bring past a boil until you see protein solids and it begins to brown, about 5 to 7 minutes. (There will be white bits on the top, and will drop to the bottom on the pan.) Remove the pan from the stove and let the butter finish browning in the pan while it cools. Don't worry if the butter gets dark, as long as it smells good (and isn't burnt) it will taste good.
Whisk the sugar, corn syrup, and vanilla into the eggs
in the mixer. Use a spatula
to scrape the bowl periodically to ensure the ingredients on the bottom and sides of the bowl are incorporated. Slowly, add the browned butter until it's incorporated into the egg mixture.
Put about a tablespoon of filing into each pop shell. Arrange on a baking sheet and bake for 17 to 20 minutes, turning halfway through. The filling should look set and no longer bubbling when completely baked. Remove the pan from the oven and allow the pie pops to cool completely before enjoying.