To make the dough: Process the almonds in a food processor for exactly 30 seconds. Transfer the ground almonds to a large mixing bowl (heatproof bowl), add the sea salt, and whisk together to combine the dry ingredients.
In a medium pot over medium heat, mix together the cane sugar, butter, cream, and corn syrup with a high heat spatula, and cook 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 to combine the wet ingredients. Last, 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 the prepared baking sheets (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 goldenbrown. Let cool com pletely on the cookie sheets.
To make the filling: In the bowl of a stand mixer fitted with the paddle attachment, add the powdered sugar, butter, molasses, cream, cinnamon, cloves, and ginger. Mix on low speed until combined, increase the speed to high, and mix for 1 minute more, or until light and fluffy. 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.