To make the dough: Process the almonds in a food processor for exactly 30 seconds. Transfer the ground almonds to a plastic mixing bowl, add the sea salt, and whisk together to combine the dry ingredients.
In a medium pot add together the cane sugar, butter, cream, and corn syrup. Cook over medium heat with a high heat spatula until the sugar is dissolved.
Continue to cook, stirring occasionally, until the mixture reaches 197°F to 200°F on a digital thermometer. Immediately remove from the heat. Pour the hot sugar mixture over the almonds, and stir several times. Add the vanilla extract, and stir to combine completely.
Let the mixture rest at room temperature for about 15 minutes, until it has cooled enough to touch.
Preheat the oven to 350°F. Line 4 cookie sheets with parchment paper.
Using your hands, form the dough into 44 balls and place them on each prepared baking sheet (11 should fit on each cookie sheet): line up 3 balls of dough along each long side of the cookie sheet, then zigzag 5 additional balls of dough down the middle.
Bake for 11 minutes, or until golden brown. Let cool completely on the cookie sheets.
To make the filling: In the bowl of a stand mixer fitted with the paddle attachment (or any electric mixer works), add the powdered sugar, butter, cocoa, peanut butter, and milk.
Mix on low until combined, increase the speed to medium speed, then to high speed, and mix for 2 to 3 minutes more, or until light and fluffy. Make sure to scrape down the sides of the bowl part way through mixing to ensure the frosting is smooth and creamy. Transfer the filling to a piping bag fit ted with Ateco tip #864.
Pair the cookies together by size, and turn over every other one. Pipe a swirl of frosting onto each turned over cookie, starting around the outer edge and spiraling into the middle. Care fully sandwich the pairs.
Store in a cool dry place for up to 3 days, or in the refrigerator for up to 7 days.