Preheat the oven to 400°F. Line a baking sheet with parchment paper and set it aside.
In a medium mixing bowl, stir together 3.5 cups sweetened shredded coconut, 2.5 tablespoons corn starch, 3/4 cup sweetened condensed milk, 1/2 teaspoon almond extract, and 1 teaspoon vanilla extract until evenly combined.
Let the mixture sit for 3 to 5 minutes.
Using 2 tablespoons, drop the mixture by heaping rounded spoonfuls onto the prepared parchment-lined baking sheet, spacing the mounds about 1 inch apart.
Bake in the preheated oven for 15 to 20 minutes, watching closely, until the cocadas are lightly golden brown.
Remove the baking sheet from the oven and transfer the cocadas to a wire rack to cool completely.
Once cooled, dust the cocadas with 1/4 cup confectioners' sugar using a fine-mesh sieve or sifter.
Store the cookies loosely covered at room temperature until ready to use.