Preheat the oven to 350°F. Line baking sheets with parchment paper and set aside.
Use mixer with paddle attachment or beaters to cream together butter, brown sugar, and granulated sugar until light and fully (about 2 to 3 minutes). Scrape down the mixing bowl then add the eggs, vanilla extract, and almond extract and beat until combined, pausing and scraping the bowl down, as needed.
Meanwhile, whisk together the flour, baking powder, and sea salt.
Add half the flour mixture to the butter mixture and beat until incorporated then stir in the other half of flour mixture by hand until cookie dough forms. Cover and chill the dough for at least 30 minutes.
To make the sweet potato pie custard filling: Combine the sweet potato puree, egg yolk, brown sugar, granulated sugar, melted butter, heavy cream, vanilla extract, cinnamon, nutmeg, and sea salt until uniform.
Divide dough into 16 equal roughly pieces then roll into balls. Place the dough balls on prepared baking sheets, leaving at least two inches between each, then use a large measuring cup to flatten one ball then a smaller measuring cup to press a well into the middle, leaving about a ½ inch "lip" around the well. Repeat with all cookie dough balls, dipping the measuring cups in flour between each one to prevent sticking.
Spoon and spread filling into the middle of each cookie dough round.
Transfer pans to oven and bake for 10 to 12 minutes, or until the cookies set and the edges begin to brown.
Cool for 5 minutes before removing to a wire rack to cool completely.